PARENT AGREEMENT


                                      among


                         LYONDELL PETROCHEMICAL COMPANY,

                            MILLENNIUM CHEMICALS INC.

                           AND EQUISTAR CHEMICALS, LP









                                TABLE OF CONTENTS
                                -----------------

                                                                            Page

SECTION 1           GUARANTEE OF OBLIGATIONS...................................2
         1.1        Guarantee..................................................2
         1.2        Guarantee Regarding Interested Owner Agreements............2
         1.3        No Demand or Notice........................................3
         1.4        Waiver of Resort to Security...............................3
         1.5        No Discharge...............................................3
         1.6        Waivers by the Parent......................................3
         1.7        No Reduction...............................................4
         1.8        Enforcement................................................4
         1.9        Continued Effectiveness.  .................................4
         1.10       Certain Defenses...........................................4
         1.11       Parties in Interest. ......................................4

SECTION 2           OWNERSHIP AND BUSINESS OF PARTNER SUBS.....................5
         2.1        Restrictions on Transfer and Pledge of Partner Sub Stock...5
         2.2        Right of First Option......................................6
         2.3        Prohibition on Affiliated Obligor Bankruptcy, Etc..........8
         2.4        Special Purpose Subsidiaries. .............................8

SECTION 3           STANDSTILL AGREEMENT.......................................8
         3.1        Standstill.................................................8
         3.2        Exceptions.................................................9

SECTION 4           MISCELLANEOUS.............................................10
         4.1        No Waivers................................................10
         4.2        Expenses in Connection with Exercise.  ...................10
         4.3        Subordination.............................................10
         4.4        Confidentiality and Use of Information....................10
         4.5        Competing Businesses......................................10
         4.6        Further Assurances........................................11
         4.7        Successors and Assigns.  .................................11
         4.8        Benefits of Agreement Restricted to the Parties...........11
         4.9        Notices...................................................11
         4.10       Severability..............................................12
         4.11       Termination...............................................12
         4.12       Construction and Certain Definitions......................12
         4.13       Counterparts..............................................13
         4.14       Governing Law.............................................13
         4.15       Jurisdiction; Consent to Service of Process; Waiver.......13
         4.16       Waiver of Jury Trial......................................13
         4.17       Dispute Resolution........................................13
         4.18       Amendment.................................................13

APPENDICES

Appendix A          List of Related Agreements
Appendix B          Dispute Resolution Procedures








                                PARENT AGREEMENT
                                ----------------


         This Parent Agreement (this  "Agreement") is made as of this 1st day of
December,  1997 among Lyondell  Petrochemical  Company,  a Delaware  corporation
("Lyondell"),  Millennium Chemicals Inc., a Delaware  corporation  ("Millennium"
and,  together with  Lyondell,  the  "Parents")  and Equistar  Chemicals,  LP, a
Delaware limited partnership (the "Partnership").

         WHEREAS,  Lyondell and Millennium  entered into the Master  Transaction
Agreement  dated  as of July 25,  1997,  as  amended  (the  "Master  Transaction
Agreement").

         WHEREAS, Lyondell Petrochemical G.P. Inc. ("Lyondell  GP") and Lyondell
Petrochemical  L.P.  Inc.  ("Lyondell  LP" and,  together  with Lyondell GP, the
"Lyondell  Partner Subs") are both Delaware  corporations and direct or indirect
wholly owned subsidiaries of Lyondell.

         WHEREAS,   Millennium  Petrochemicals  GP  LLC  ("Millennium  GP")  and
Millennium  Petrochemicals LP LLC ("Millennium LP" and, together with Millennium
GP, the "Millennium Partner Subs") are both Delaware limited liability companies
and direct or indirect wholly owned subsidiaries of Millennium.

         WHEREAS, pursuant to the terms of the Master Transaction Agreement, the
Partnership has been formed under the laws of the State of Delaware  pursuant to
the Limited Partnership Agreement being entered into simultaneously herewith (as
it may in the future be amended, supplemented, restated or otherwise modified or
amended, the "Partnership Agreement"), with Lyondell GP and Millennium GP as the
general  partners and Lyondell LP and ML Partner as the limited  partners of the
Partnership.  The  Lyondell  Partner  Subs,  together  with any other  direct or
indirect subsidiary of Lyondell that is a party to any of the Related Agreements
(as  defined  herein),  are  referred  to  herein  as the  "Lyondell  Affiliated
Obligors."  The  Millennium  Partner  Subs,  together  with any other  direct or
indirect  subsidiary  of  Millennium  that  is a  party  to any  of the  Related
Agreements,  are referred to herein as the "Millennium Affiliated Obligors." The
Lyondell   Affiliated   Obligors  and  the   Millennium   Affiliated   Obligors,
collectively or individually as the context may require,  are referred to herein
as the  "Affiliated  Obligors."  The Lyondell  Partner  Subs and the  Millennium
Partner  Subs,  collectively  or  individually  as the context may require,  are
referred to herein as the "Partner Subs."

         WHEREAS,  in  connection  with the  closing of the  transactions  to be
effected pursuant to the Master Transaction  Agreement,  the Parents and certain
of their respective  affiliates,  have entered into or are entering into various
agreements  and other legal  documents,  including  the  Partnership  Agreement,
services agreements and asset contribution agreements (including this Agreement,
the  "Related  Agreements"),   each  of  which  is  integrally  related  to  the
capitalization  and  future  operations  of the  Partnership  and is  listed  on
Appendix A hereto.  The Related  Agreements  (other than this Agreement) and any
additional  agreements  that may from time to time be added to Appendix A hereto
by agreement of the Parents, as they may in the future be amended, supplemented,
restated  or  otherwise   modified,   are  referred  to  herein  as  the  "Other
Agreements."






                                                     
         WHEREAS, this Agreement is essential to the consummation of the closing
pursuant  to  the  Master  Transaction  Agreement  and  the  entering  into  and
effectiveness  of the  Other  Agreements,  and  each  of  the  parties  to  such
agreements is relying on this Agreement in connection with entering into each of
the Other Agreements.

         WHEREAS, in order to induce the parties thereto to enter into the Other
Agreements,  each Parent is willing, solely for the benefit of the Beneficiaries
(as  defined  below in  Section  1.11)  and their  successors  and  assigns,  to
guarantee the performance by its Affiliated  Obligors of the obligations of such
Affiliated Obligors as set forth in this Agreement.

         WHEREAS,  each  Parent is willing to subject  the Partner Sub Stock (as
defined  herein)  to  certain  restrictions  on  transfer,  as set forth in this
Agreement.

         NOW  THEREFORE,  in,  consideration  of the  foregoing  and the  mutual
promises and covenants of the parties  hereto,  the Parents and the  Partnership
hereby agree as follows:


                                    SECTION 1
                            GUARANTEE OF OBLIGATIONS
                            ------------------------

         1.1  Guarantee.  Each Parent  hereby  unconditionally,  absolutely  and
irrevocably  guarantees,  undertakes and promises to cause, as herein  provided,
the due and  punctual  payment  and  the  full  and  prompt  performance  by its
Affiliated  Obligors  of all of the  amounts to be paid and all of the terms and
provisions  to be  performed  or  observed  by or on the part of its  Affiliated
Obligors  under the Other  Agreements in accordance  with the terms thereof (all
such terms and  provisions as now or hereafter in existence  being  collectively
called the "Obligations") as follows:  in the event that its Affiliated Obligors
shall  fail in any manner  whatsoever  to pay,  perform or observe  any of their
Obligations,  when and as the same shall be  required to be paid,  performed  or
observed under the terms of the Other  Agreements,  such Parent will itself duly
and punctually  pay, or fully and promptly  perform or observe,  as the case may
be, such Obligations, or cause the same to be duly and punctually paid, or fully
and promptly  performed or observed,  in each case as if such Parent were itself
the obligor with respect to such Obligations under the Other Agreements. Insofar
as this Section 1.1 relates to the  obligations  of an Affiliated  Obligor under
the  Partnership  Agreement  and except as set forth in Section  1.2,  no Parent
shall be required to make, or cause a Partner Sub to make, any  contribution  to
the Partnership that such Partner Sub is not otherwise required to make pursuant
to the terms of Section 2.3, 2.4, or 12.2(d)(ii) of the  Partnership  Agreement.
Insofar  as this  Section  1.1  applies  to  Other  Agreements  other  than  the
Partnership  Agreement,  the term  "Affiliated  Obligors"  will not  include the
Partnership nor any partner in the Partnership in its capacity as such.

         1.2  Guarantee  Regarding  Interested  Owner  Agreements.  Each  Parent
acknowledges   that  the  Partnership   Agreement  sets  forth   definitions  of
"Conflicted   Partner"  and   "Nonconflicted   Partner,"  and  provides  that  a
Nonconflicted  Partner has certain  exclusive  rights to control the Partnership
with  respect  to any  Conflict  Circumstance  (as  defined  in the  Partnership
Agreement);  and  accordingly,  without  limiting  the rights of its Partner Sub
under  Section 6.8 of the  Partnership  Agreement,  each Parent hereby agrees to
cause its Partner Sub (i) to cause the  Partnership to pay,  perform and observe
all of the  Obligations  to be paid,  performed or observed by or on the part of
the  Partnership  under  the  Other  Agreements,  in  accordance  with the terms
thereof, to the extent that such Partner Sub is the Nonconflicted Partner and is
thereby  entitled  to cause the  payment,  performance  and  observance  of such
Obligations  and (ii) to abide by its obligations as the  Nonconflicted  Partner
with respect to any Conflict  Circumstance  in accordance  with the terms of the
Partnership Agreement applicable thereto; provided,  however, that each Parent's
responsibility  under this Section 1.2 for a failure of the  Partnership to pay,
perform or observe its obligations  under the Other  Agreements shall be limited
to the  circumstances in which the  Partnership's  failure to so pay, perform or
observe its obligations under the Other Agreements was directly caused by an act
or failure to act of its Partner Sub;  provided,  further,  that nothing in this
Section 1.2 shall require a Parent to make or cause such Partner Sub to make any
contribution to the Partnership that such Partner Sub is not otherwise  required
to make  pursuant  to  Section  2.3,  2.4,  or  12.2(d)(ii)  of the  Partnership
Agreement.

         1.3 No Demand or Notice.  It shall not be a condition to the guarantees
and  agreements  set  forth  in  Sections  1.1  and  1.2  above  (together,  the
"Guarantee")  that a Beneficiary  shall have first made any request of or demand
upon,  or given  any  notice  of the  occurrence  of a  default  under the Other
Agreements or any other notice  whatsoever  to, either Parent or its  Affiliated
Obligors or any other Person,  or shall have instituted any action or proceeding
against any Affiliated Obligor or any other Person in respect thereof,  or shall
have  joined any  Affiliated  Obligor or the  Partnership  in any such action or
proceeding.  A Beneficiary in asserting the benefit of the Guarantee  shall give
prompt  notice to a Parent of any  failure  by its  Affiliated  Obligors  or the
Partnership to pay, perform or observe any Obligation;  provided,  however, that
any  failure,  delay or defect in the giving of such  notice  shall not alter or
affect the Guarantee under this Agreement.

         1.4 Waiver of Resort to Security.  Each Parent further agrees that this
Agreement,  insofar as it  constitutes  a  guarantee  of  monetary  Obligations,
constitutes  a guarantee  of payment  when due and not of  collection,  and each
Parent  waives any right to require as a  condition  to its  Guarantee  that any
resort be had by a  Beneficiary  to any  security  held for the  payment  of any
Obligations.

         1.5 No  Discharge.  The  Guarantee  is and shall  remain  absolute  and
unconditional irrespective of any circumstance that might otherwise constitute a
legal or equitable discharge of a surety or guarantor,  as the case may be, with
respect to its Guarantee.

         1.6 Waivers by the Parent.  Each Parent hereby waives,  with respect to
the Guarantee but without  prejudice to the rights of the parties to the several
Other   Agreements,   any  notice  of  acceptance  of  this  Agreement,   grace,
presentment,  demand,  protest,  notice of the occurrence of a default under the
Other  Agreements and any other notice of any kind  whatsoever and promptness in
making any claim or demand hereunder. The Guarantee shall not be affected by (i)
the  failure of a  Beneficiary  to assert any claim or demand or to enforce  any
right or remedy  under the  provisions  of any of the  Other  Agreements  or any
agreement related thereto or otherwise,  (ii) any extension or renewal of any of
the Other  Agreements or any agreement  related  thereto,  (iii) any rescission,
waiver,  amendment or  modification  of any of the terms or provisions of any of
the Other  Agreements or of any agreement  related thereto,  including,  without
limitation, any change in the time, manner or place of payment or performance of
any of the obligations  under the Other  Agreements,  or (iv) the release of any
security held for payment of any Obligations.

         1.7 No Reduction.  The Guarantee shall not be subject to any reduction,
limitation,  impairment  or  termination  for  any  reason,  including,  without
limitation, any claim of waiver, release,  surrender,  alteration or compromise,
and shall not be subject to any defense or set-off, counterclaim,  recoupment or
termination whatsoever, except as provided in Section 1.10.

         1.8  Enforcement.  Notwithstanding  anything herein to the contrary,  a
Beneficiary  may  proceed to enforce the  Guarantee  without  first  pursuing or
exhausting  any right or remedy that it or any of its  successors or assigns may
have against any Affiliated Obligor or either Parent or any other person.

         1.9  Continued  Effectiveness.  The  Guarantee  shall  continue  to  be
effective or be reinstated,  as the case may be, if at any time payment,  or any
part thereof,  of any  Obligation of an Affiliated  Obligor is rescinded or must
otherwise be restored or returned by the Person  receiving such payment upon the
insolvency, bankruptcy or reorganization of an Affiliated Obligor, all as though
such payment or part thereof had not been made.

         1.10  Certain  Defenses.  Nothing  herein is intended to deny to either
Parent,  and it is expressly  agreed that each Parent shall have and may assert,
any and all of the  defenses,  set-offs,  counterclaims  and other rights (other
than those relating to insolvency,  bankruptcy or reorganization as described in
Section 1.9) with regard to any  Obligations  that its  Affiliated  Obligors may
possess except any defense its Affiliated  Obligors may possess relating to lack
of validity or  enforceability of the Other Agreements or any other agreement or
instrument  relating thereto as against its Affiliated Obligors arising from the
defective  incorporation  or  other  defective  organization  of its  Affiliated
Obligors,  their  lack  of  qualification  to  do  business  in  any  applicable
jurisdiction or their defective corporate or other  organizational  authority to
enter into, deliver or perform the Other Agreements.

         1.11  Parties in  Interest.  This  Agreement  shall inure solely to the
benefit  of the  Beneficiaries,  each  of whom  has the  right  to  enforce  the
Guarantee  against  the  Parents,  and  nothing  in this  Agreement,  express or
implied,  is  intended  to or shall  confer  upon any other  Person any  rights,
benefits  or  remedies  of any  nature  whatsoever  under or by  reason  of this
Agreement.  As used in this Agreement,  "Beneficiaries" shall mean (i) as to any
obligations  of Millennium  hereunder,  except for its  obligations  pursuant to
Section 1.1 hereof with respect to the Partnership  Agreement,  the Partnership,
Lyondell and the Lyondell  Affiliated  Obligors,  (ii) as to any  obligations of
Lyondell  hereunder,  except for its obligations  pursuant to Section 1.1 hereof
with respect to the Partnership Agreement,  the Partnership,  Millennium and the
Millennium Affiliated Obligors, and (iii) as to any obligations of Millennium or
Lyondell  pursuant  to  Section  1.1  hereof  with  respect  to the  Partnership
Agreement, Lyondell and Millennium, respectively. As used in this Agreement, the
term Parent  includes any successor or  transferee  of the Parent,  and the term
Affiliated  Obligors  includes any successor to or transferee of the  Affiliated
Obligors'  interest in the  Partnership  permitted  pursuant to the  Partnership
Agreement.


                                    SECTION 2
                     OWNERSHIP AND BUSINESS OF PARTNER SUBS
                     --------------------------------------

         2.1  Restrictions on Transfer and Pledge of Partner Sub Stock. (a) Each
Parent  agrees that except as  otherwise  provided  below in this Section 2.1 or
Section 2.2 or with the written  consent of the other  Parent (or any  Successor
Parent, as defined in Section 2.1(d)),  which consent may be granted or withheld
in such Parent's sole  discretion,  it will not, in any transaction or series of
transactions,  directly or  indirectly,  (i) sell,  assign or  otherwise  in any
manner  dispose of, whether by act, deed,  merger or otherwise  ("Transfer")  or
(ii) mortgage, pledge, encumber or create or suffer to exist any pledge, lien or
encumbrance  upon or  security  interest in  ("Pledge"),  all or any part of the
capital stock (including any securities  convertible into or exchangeable for or
carrying any rights to  purchase,  subscribe  for or otherwise  acquire any such
capital  stock) of its Partner  Subs  (collectively,  the  "Partner Sub Stock").
(Each of the defined terms "Transfer"and  "Pledge" is used herein both as a noun
and as a verb.) Any  attempt by a Parent to  Transfer or Pledge all or a portion
of its Partner Sub Stock in violation of this Agreement  shall be void ab initio
and shall not be  effective  to transfer  such  Partner Sub Stock or any portion
thereof. The Partnership  Agreement contains provisions relating to the Transfer
and Pledge of the Partner Subs' direct interests in the Partnership.

         (b) The Parent  agrees  that all  certificates  representing  shares of
Partner Sub Stock,  whether currently owned or hereafter  acquired,  shall carry
the  following  legend,  which  legend each Parent  agrees to cause to be placed
thereon and to cause to remain thereon as long as such shares are subject to the
restrictions of this Agreement:

         THE SALE, ASSIGNMENT,  PLEDGE OR OTHER TRANSFER OR HYPOTHECATION OF THE
         STOCK   REPRESENTED   BY  THIS   CERTIFICATE   IS  SUBJECT  TO  CERTAIN
         RESTRICTIONS  PURSUANT TO AND MAY NOT BE EFFECTED  EXCEPT IN ACCORDANCE
         WITH THE PROVISIONS OF AN AGREEMENT BINDING UPON THE OWNER OF THE STOCK
         REPRESENTED  HEREBY.  THE OWNER OR ISSUER  WILL  FURNISH A COPY OF SUCH
         AGREEMENT TO ANY PROPOSED  TRANSFEREE  OR PLEDGEE  WITHOUT  CHARGE UPON
         REQUEST.

         (c)  Without  the need for the  consent of any  Person,  any Parent may
Transfer its Partner Sub Stock to any wholly-owned Affiliate of such Parent.

         (d) Each Parent may Transfer all (but not less than all) of its Partner
Sub Stock if such  Transfer is in connection  with (i) a merger,  consolidation,
conversion or share exchange of such Parent or (ii) a sale or other  disposition
of (x) the Partner Sub Stock plus (y) other assets  representing  at least fifty
percent  (50%) of the book value of such Parent's  assets  excluding the Partner
Sub Stock,  as reflected on its most recent audited  consolidated  (or combined)
financial  statements;  provided,  however,  the ultimate  parent  entity of the
acquiring,   succeeding  or  surviving  entity  in  any  such  transaction  (the
"Successor  Parent") (i) shall  succeed to and be  substituted  for such Parent,
with the same  effect as if it had been named  herein and (ii) shall  execute an
instrument  wherein such  ultimate  parent entity shall agree to be bound by the
obligations of such Parent under this  Agreement,  with the same effect as if it
had been named  herein,  whereupon,  unless such Parent shall become a direct or
indirect  subsidiary of the  Successor  Parent,  such Parent shall  thereupon be
released from all obligations hereunder.

         (e) Nothing in this  Agreement  shall prevent the Transfer or Pledge of
the capital stock,  equity ownership  interests or other securities of a Parent,
and no such Transfer or Pledge of securities  issued by a Parent shall be deemed
to constitute a Transfer or Pledge of Partner Sub Stock hereunder.

         (f) Each  Parent may Pledge all (but not less than all) of its  Partner
Sub Stock to any one or more Approved Lenders; provided that the Pledge shall be
evidenced by an instrument,  reasonably satisfactory to the Partnership, wherein
the  Approved  Lender  receiving  such Pledge shall agree that in the event such
Approved  Lender  obtains a right of  foreclosure  on such Parent's  Partner Sub
Stock,  such Approved  Lender will foreclose on the Partner Sub Stock of each of
such  Parent's  Partner  Subs equally so that such  Approved  Lender will in all
events hold equal portions of Partner Sub Stock of LG Partner and Lyondell LP or
Millennium GP and Millennium LP, as the case may be. An "Approved  Lender" shall
be any bank, insurance company,  investment bank or other financial  institution
that is regularly engaged in the business of making loans.

         2.2      Right of First Option.

                  (a) Without the consent of the other  Parent,  neither  Parent
may  Transfer  less than all of its Partner Sub Stock.  Unless such  Transfer is
otherwise permitted by Section 2.1, any Parent desiring to Transfer (pursuant to
a cash sale) all of its  Partner  Sub Stock (the  "Selling  Parent")  shall give
written notice (the "Initial  Notice") to the  Partnership  and the other Parent
(the "Offeree  Parent")  stating that the Selling Parent desires to Transfer its
Partner  Sub Stock and stating  the cash  purchase  price and all other terms on
which it is willing to sell (the "Offer  Terms").  Delivery of an Initial Notice
shall constitute the irrevocable offer of the Selling Parent to sell its Partner
Sub Stock to the Offeree Parent hereunder.

                  (b) The Offeree  Parent shall have the option,  exercisable by
delivering  written  notice (the  "Acceptance  Notice") of such  exercise to the
Selling  Parent  within 45 days of the date of the Initial  Notice,  to elect to
purchase  all of the Partner Sub Stock of the Selling  Parent on the Offer Terms
described  in the Initial  Notice.  The  Acceptance  Notice shall set a date for
closing  the  purchase,  such  date to be not less than 30 nor more than 90 days
after delivery of the Acceptance Notice; provided that such time period shall be
subject to extension as  reasonably  necessary (up to a maximum of an additional
120 days after such 90 day period) in order to comply with any applicable filing
and  waiting  period   requirements   under  the   Hart-Scott-Rodino   Antitrust
Improvements  Act. The closing shall be held at the Partnership's  offices.  The
purchase price for the Selling  Parent's Partner Sub Stock shall be paid in cash
delivered at the closing.  The purchase shall be consummated by appropriate  and
customary documentation  (including the giving of representations and warranties
substantially  similar to those set forth in  Sections  2.1  through  2.4 of the
Master  Transaction  Agreement  and  customary  representations  and  warranties
regarding the Selling Parent's title to its Partner Sub Stock).

                  (c) If the  Offeree  Parent  does not  elect to  purchase  the
Selling  Parent's  Partner  Sub Stock  within 45 days  after the  receipt of the
Initial Notice, the Selling Parent shall have a further 180 days during which it
may, subject to Sections 2.2(d) and (e),  consummate the sale of its Partner Sub
Stock to a third  party  purchaser  at a purchase  price and on such other terms
that are no more favorable to such  purchaser than the Offer Terms.  If the sale
is not completed within such further 180-day period, the Initial Notice shall be
deemed to have  expired and a new notice and offer shall be required  before the
Selling Parent may make any Transfer of its Partner Sub Stock.

                  (d) Before the Selling Parent may consummate a Transfer of its
Partner  Sub  Stock to a third  party in  accordance  with this  Agreement,  the
Selling Parent shall demonstrate to the Partnership that such proposed purchaser
(or the Person  willing to serve as its  guarantor  as  contemplated  by Section
2.2(f)) has outstanding  indebtedness  that is rated  investment grade by either
Moody's  Investor  Services  Inc. or Standard & Poor's  Corporation,  or if such
proposed purchaser (or such other Person) has no rated indebtedness outstanding,
such Person shall  provide an opinion from a  nationally  recognized  investment
banking firm that it could be reasonably expected to obtain such a rating.

                  (e) Notwithstanding  the foregoing  provisions of this Section
2.2, a Parent may Transfer its Partner Sub Stock (other than pursuant to Section
2.1) only if all of the following occur:

                           (i) The  Transfer  is  accomplished  in a  non-public
                  offering in compliance with, and exempt from, the registration
                  and  qualification  requirements  of  all  federal  and  state
                  securities laws and regulations.

                           (ii) The Transfer  does not cause a default under any
                  material  contract to which the  Partnership  is a party or by
                  which the Partnership or any of its properties is bound.

                           (iii)  The   transferee   executes   an   appropriate
                  agreement to be bound by this Agreement.

                           (iv)  The  transferor  and/or  transferee  bears  all
                  reasonable  costs  incurred by the  Partnership  in connection
                  with the Transfer.

                           (v)  The   transferee   (or  the   guarantor  of  the
                  obligations  of the  transferee)  satisfies  the  criteria set
                  forth in Section 2.2(d) and delivers an agreement to the other
                  Parent and the Partnership  substantially  in the form of this
                  Agreement.

                           (vi) The proposed transferor is not in default in the
                  timely  performance of any of its material  obligations to the
                  Partnership.

                           (vii) The provisions of Section 2.2(f) are satisfied.

                  (f)  Neither  Parent may  Transfer  the  Partner  Sub Stock of
either of its  Partner  Subs to any Person  unless  such  Parent  simultaneously
Transfers  the  Partner  Sub Stock of its other  Partner Sub to such Person or a
wholly-owned Affiliate (as defined in the Partnership Agreement) of such Person.

         2.3  Prohibition  on Affiliated  Obligor  Bankruptcy,  Etc. Each Parent
hereby agrees that it will not, without the written consent of the other Parent,
permit any of its  Affiliated  Obligors (or their  successors or assigns) (i) to
commence  a  voluntary  action  under the  Federal  bankruptcy  laws,  as now or
hereafter  constituted,  or any other  applicable  Federal or State  bankruptcy,
insolvency  or  other  similar  law,  (ii)  to  institute  a  proceeding  to  be
adjudicated a voluntary bankrupt, (iii) to consent to the filing of a bankruptcy
proceeding  against it, (iv) to fail to contest a bankruptcy  proceeding against
it, (v) to consent to the  appointment of a receiver,  custodian,  liquidator or
trustee for it or for all or any  substantial  portion of its property,  (vi) in
the case of its Partner  Subs, to issue or sell other than to such Parent any of
its own Partner Sub Stock or (vii) to effect,  recognize  or permit any transfer
of any of its own Partner Sub Stock other than in accordance with the provisions
of Section 2 of this Agreement.

         2.4  Special  Purpose  Subsidiaries.  Each  Parent  agrees that (i) the
business of its Partner  Subs shall be  restricted  solely to the holding of the
respective  interests in the  Partnership  and the doing of things  necessary or
incidental in connection therewith,  and (ii) it will cause its Partner Subs not
to own any assets, incur any liabilities or engage, participate or invest in any
business  outside  the scope of their  businesses  as  described  in clause (i);
provided,  however,  that this  Section 2.4 shall not apply with  respect to any
Wholly  Owned  Affiliates  to  whom  such  Partner  Subs  shall  transfer  their
respective  interests in the Partnership if such Wholly Owned Affiliates are not
bound by Section 9.6 of the Partnership Agreement.


                                    SECTION 3
                              STANDSTILL AGREEMENT
                              --------------------

         3.1  Standstill.  Each Parent agrees that,  until the  expiration of 24
months from the date on which either such Parent and its Affiliates or the other
Parent and its Affiliates no longer hold an interest in the Partnership, neither
it, nor any of its Affiliated  Obligors or other  subsidiaries,  shall,  without
prior written approval of the other Parent: (i) in any manner acquire,  agree to
acquire or make any proposal to acquire, directly or indirectly, any securities,
assets or property of the other  Parent  (other than such  Parent's  Partner Sub
Stock or the interests in the Partnership  held by such Parent's  Partner Subs),
whether  such  agreement  or proposal  is made with or to the other  Parent or a
third  party;  (ii) make any  unsolicited  proposal to enter  into,  directly or
indirectly, any merger or other business combination involving the other Parent;
(iii)  make,  or  in  any  way  participate,  directly  or  indirectly,  in  any
"solicitation"  of  "proxies"  (as such terms are used in the proxy rules of the
Securities and Exchange  Commission) to vote, or seek to advise or influence any
person with respect to the voting of, any voting securities of the other Parent;
(iv) form,  join or in any way  participate in a "group"  (within the meaning of
Section  13(d)(3) of the  Securities  Exchange  Act of 1934) with respect to any
voting  securities of the other Parent;  (v) otherwise  act, alone or in concert
with others, to seek to control or influence the management,  Board of Directors
or  policies of the other  Parent  (other  than with  respect to the  ownership,
business, property and affairs of the Partnership); (vi) disclose any intention,
plan or arrangement inconsistent with the foregoing; or (vii) advise, encourage,
provide assistance  (including financial assistance) to or hold discussions with
any other  persons in  connection  with any of the  foregoing.  Each Parent also
agrees  during  such  period  not to:  (i)  request  the  other  Parent  (or its
directors,  officers,  employees or agents), directly or indirectly, to amend or
waive any provision of this Section 3.1 (including this sentence);  or (ii) take
any action  which might  reasonably  be expected to require the other  Parent to
make a public announcement  regarding the possibility of a business  combination
or merger.

         3.2      Exceptions.  Notwithstanding the provisions of Section 3.1:

         (a) Either Parent may, by notice to the other, terminate the provisions
of Section 3.1 (as applied to both Parents) at any time within 30 days after the
occurrence of any of the following events with respect to the other Parent:  (i)
a Change of Control (as defined below) of such other Parent shall have occurred,
(ii) such other Parent shall have entered into a definitive  agreement providing
for, or publicly announced its intention to effect, any transaction  involving a
Change of Control of such other Parent or (iii) a tender offer or exchange offer
shall have been commenced or publicly announced that, if consummated, would have
the effect  with  respect to such other  Parent  described  in clause (c) of the
definition  of "Change of Control." A "Change of Control" of a Parent shall mean
the  occurrence of any of the following  events:  (a) there shall be consummated
any  consolidation,  merger or share  exchange  of such Parent (i) in which such
Parent is not the  continuing or surviving  Person (other than a  consolidation,
merger or share exchange with a wholly owned  subsidiary of such Parent in which
all shares of common stock of such Parent  outstanding  immediately prior to the
effectiveness  thereof  are  changed  into or  exchanged  for the same number of
shares of common stock of such  subsidiary) or (ii) pursuant to which the common
stock of such Parent is converted into cash, securities or other property, other
than, in each case, a consolidation,  merger or share exchange of such Parent in
which the holders of the common stock  immediately  prior to the  consolidation,
merger or share  exchange hold,  directly or indirectly,  at least a majority of
the  voting  power and  common  equity of the  continuing  or  surviving  Person
immediately  after  such  consolidation,  merger  or  share  exchange;  (b) such
Parent's  properties and assets are sold or otherwise  disposed of substantially
as an entirety on a consolidated  basis to any Person or group of Persons in any
one transaction or a series of related transactions,  other than as contemplated
by the Master  Transaction  Agreement;  or (c) any Person or any Persons  acting
together  which would  constitute  a "group" (as defined in Section  3.1) (other
than such Parent,  any  subsidiary of such Parent,  any employee  stock purchase
plan,  stock option plan or other stock  incentive  plan or program,  retirement
plan or automatic dividend  reinvestment plan or any substantially  similar plan
of such Parent or any subsidiary of such Parent or any Person holding securities
of such Parent for or pursuant to the terms of any such employee  benefit plan),
together with any affiliates  thereof,  shall acquire  beneficial  ownership (as
defined in Rule 13d-3 under the Securities  Exchange Act of 1934) of 50% or more
of the voting stock of such Parent.

         (b) The  terms of the  first  sentence  of  Section  3.1  shall  not be
applicable  to the  purchase and sale of any  securities  of the other Parent by
independent  third-party  managers  of any  pension  or other  related  employee
benefit plans who are acting as passive investors in the other Parent.


                                    SECTION 4
                                  MISCELLANEOUS
                                  -------------

         4.1 No  Waivers.  No failure or delay by a  Beneficiary  or a Parent in
exercising  any right or power  under this  Agreement,  or any single or partial
exercise  of any such  right or  power,  shall  preclude  any  other or  further
exercise  thereof or the  exercise of any other  right or power.  Such single or
partial  exercise of any right or power shall be cumulative and not exclusive of
any rights or remedies provided by law.

         4.2 Expenses in  Connection  with  Exercise.  In the event of a dispute
between  parties  hereto  regarding  the exercise or  enforcement  of any of the
rights of a  Beneficiary  under  this  Agreement  or the  failure by a Parent to
perform or observe any of the provisions of this Agreement,  the party that does
not ultimately  prevail in such dispute shall be liable,  and hereby agrees,  to
reimburse,  on demand, each other such party for any and all costs and expenses,
including  the fees and  expenses  of legal  counsel  and of any other  counsel,
experts,  consultants  or agents,  that such other party may incur in connection
therewith.

         4.3  Subordination.  The  rights  of a Parent  against  its  Affiliated
Obligors  arising from any payment or performance by a Parent hereunder shall be
subordinate  in all  respects to the rights of the  Beneficiaries  against  such
Affiliated  Obligors,  and  such  Parent  shall  not  compete  in any way with a
Beneficiary in any winding-up or dissolution of such Affiliated  Obligors unless
and until all sums due and to become due from such  Affiliated  Obligors  to the
Beneficiaries have been paid in full. If any amount shall be paid to a Parent in
violation of this Section, such amount shall be held in trust for the benefit of
the  Beneficiaries  and  shall  forthwith  be  paid to the  Beneficiaries  to be
credited and applied to any sums owed or to be owed by such Parent's  Affiliated
Obligors.  Subject to the  foregoing,  upon payment of all sums due or to become
due by Affiliated  Obligors to the Beneficiaries,  the Parent of such Affiliated
Obligors  shall be  subrogated  to the rights of the  Beneficiary  against  such
Affiliated  Obligors,  and the  Beneficiaries  agree  to  take at such  Parent's
expense  such steps as such  Parent may  reasonably  request to  implement  such
subrogation.

         4.4 Confidentiality  and Use of Information.  (a) Each Parent agrees to
be  bound  by the  terms  and  conditions  of  Section  13.1 of the  Partnership
Agreement as if such Parent was a "Partner" as defined in such agreement.

         (b) The Parents  shall consult with each other on an ongoing basis with
respect to disclosures  regarding the  Partnership  and its business and affairs
that  each is  required  to make in  reports  filed  from  time to time with the
Securities and Exchange Commission.

         4.5  Competing  Businesses.  If either  Parent  desires to  initiate or
pursue any opportunity to undertake,  engage in, acquire or invest in a Business
Opportunity (as such term is defined in the Partnership Agreement),  such Parent
agrees to offer such Business Opportunity to the Partnership under the terms and
conditions set forth in Sections 9.3(c) and (d) of the Partnership  Agreement as
if such  Parent were the  "Proposing  Partner"  (as  defined in the  Partnership
Agreement) with respect  thereto,  and in such event the Partnership  shall have
the rights and  obligations  with  respect  thereto  set forth in such  Sections
9.3(c) and (d).

         4.6  Further  Assurances.  From  time to time,  each  Parent  agrees to
execute and deliver  such  additional  documents  and  provide  such  additional
information and assistance as the Beneficiaries may reasonably  require to carry
out the terms of this Agreement.

         4.7 Successors and Assigns. Except as may be expressly provided herein,
this Agreement  shall be binding upon and inure to the benefit of the successors
of the  Beneficiaries.  Except as provided in this  Agreement  and except that a
Parent  may assign its rights or  obligations  under this  Agreement  to a third
party in connection with a transfer of direct interests in the Partnership owned
by its Partner Subs if such transfer is permitted and  consummated in accordance
with the  Partnership  Agreement,  no Parent may assign or  delegate  any of its
rights or obligations  under this Agreement without the prior written consent of
all  the  Beneficiaries,  which  consent  shall  be in  the  sole  and  absolute
discretion of such Beneficiaries. Any purported assignment or delegation without
such consent shall be void and ineffective.

         4.8 Benefits of Agreement Restricted to the Parties.  This Agreement is
made solely for the benefit of the  Beneficiaries  (as defined in Section 1.11),
and no other Person  shall have any right,  claim or cause of action under or by
virtue of this Agreement.

         4.9 Notices.  All notices,  requests,  demands and other communications
(collectively, "notices") required or may be given under this Agreement shall be
in  writing  and  shall  be  deemed  to have  been  duly  given  if and when (i)
transmitted  by  telecopier  facsimile  with  proof  of  confirmation  from  the
transmitting  machine  or (ii)  delivered  by  commercial  courier or other hand
delivery, as follows:

If to Lyondell                               If to the Lyondell Partner Subs

Lyondell Petrochemical Company               Lyondell Petrochemical Company
1221 McKinney Street                         1221 McKinney Street
Houston, Texas 77010                         Houston, Texas 77010
Attention:  Jeffrey R. Pendergraft           Atention:  Jeffrey R. Pendergraft
Telecopy Number: (713) 652-4538              Telecopy Number: (713) 652-4538


If to Millennium                            If to the Millennium Partner Subs

Millennium Chemicals Inc.                   Millennium Chemicals Inc.
99 Wood Avenue South                        99 Wood Avenue South
Iselin, New Jersey  08830                   Iselin, New Jersey  08830
Attention:  George H. Hempstead, III        Attention:  George H. Hempstead, III
Telecopy Number: (732) 603-6857             Telecopy Number: (732) 603-6857


If to the Partnership

Equistar Chemicals, LP
1221 McKinney Street
Houston, Texas 77010
Attention:  Gerald A. O'Brien
Telecopy Number:  (713) 309-4718

or to such other address as such Parent or  Beneficiary  shall have specified by
notice to the other Parent.

         4.10  Severability.  In the event that any provisions of this Agreement
shall finally be determined to be unlawful, such provision shall, so long as the
economic and legal  substance  of the  transactions  contemplated  hereby is not
affected in any  materially  adverse  manner as to any party  hereto,  be deemed
severed from this Agreement and every other  provision of this  Agreement  shall
remain in full force and effect.

         4.11 Termination. Except for Sections 3.1 and 3.2, this Agreement shall
terminate  and be of no further  force and effect as to a Parent (i) as and when
provided in Section 2.1(d) or (ii) if and when such Parent  Transfers all of its
Partner Sub Stock in a transaction permitted by Section 2.2; provided,  however,
that such termination shall not discharge (x) any accrued  Obligations owed by a
Parent  as of the  date of such  termination  or (y)  any  Obligations,  whether
arising before or after such termination, under such Parent's Asset Contribution
Agreement (as such term is defined in the Partnership  Agreement) or any Related
Agreement executed pursuant to such Asset Contribution  Agreement.  In addition,
the Guarantee by a Parent of Obligations  of an Affiliated  Obligor other than a
Partner Sub shall  terminate  as and when the Parent  ceases to own any stock of
such  Affiliated  Obligor,  insofar as such  Guarantee  relates  to  Obligations
arising thereafter.

         4.12     Construction and Certain Definitions.

         (a) In construing this  Agreement,  the following  principles  shall be
followed:  (i) no consideration  shall be given to the captions of the articles,
sections, subsections or clauses, which are inserted for convenience in locating
the  provisions  of this  Agreement and not as an aid in  construction;  (ii) no
consideration  shall be given to the fact or  presumption  that any party hereto
had a greater or lesser hand in drafting this  Agreement;  (iii)  examples shall
not be  construed  to  limit,  expressly  or by  implication,  the  matter  they
illustrate;  (iv) the word "includes" and its syntactic variants mean "includes,
but is not limited to" and corresponding syntactic variant expressions;  (v) the
plural shall be deemed to include the singular, and vice versa; (vi) each gender
shall be deemed to include the other gender; and (vii) each exhibit,  attachment
and schedule to this Agreement is a part of this Agreement.

         (b) The term "Person" shall mean any natural person or any corporation,
partnership,  limited liability company,  joint venture,  association,  trust or
other entity or organization.

         4.13  Counterparts.  This  Agreement  may be  executed  in one or  more
counterparts,  each of which shall constitute an original, and all of which when
taken together shall constitute one and the same original document.

         4.14  Governing Law. The laws of the State of Delaware shall govern the
construction,  interpretation and effect of this Agreement without giving effect
to any conflicts of law principles.

         4.15 Jurisdiction;  Consent to Service of Process; Waiver. ANY JUDICIAL
PROCEEDING  BROUGHT  AGAINST ANY PARTY TO THIS AGREEMENT OR ANY DISPUTE UNDER OR
ARISING OUT OF OR IN CONNECTION WITH THIS AGREEMENT OR ANY MATTER RELATED HERETO
SHALL BE BROUGHT IN THE FEDERAL OR STATE COURTS OF THE STATE OF  DELAWARE,  AND,
BY  EXECUTION  AND  DELIVERY  OF THIS  AGREEMENT,  EACH OF THE  PARTIES  TO THIS
AGREEMENT  ACCEPTS THE  EXCLUSIVE  JURISDICTION  OF SUCH COURTS AND  IRREVOCABLY
AGREES TO BE BOUND BY ANY JUDGMENT (AS FINALLY ADJUDICATED)  RENDERED THEREBY IN
CONNECTION  WITH THIS  AGREEMENT.  EACH OF THE PARTIES TO THIS  AGREEMENT  SHALL
APPOINT THE CORPORATION  TRUST COMPANY,  THE PRENTICE-HALL  CORPORATION  SYSTEM,
INC. OR A SIMILAR ENTITY (THE "AGENT") AS AGENT TO RECEIVE ON ITS BEHALF SERVICE
OF PROCESS IN ANY  PROCEEDING  IN ANY SUCH COURT IN THE STATE OF  DELAWARE.  THE
FOREGOING  CONSENTS TO JURISDICTION AND APPOINTMENTS OF AGENT TO RECEIVE SERVICE
OF PROCESS SHALL NOT  CONSTITUTE  GENERAL  CONSENTS TO SERVICE OF PROCESS IN THE
STATE OF  DELAWARE  FOR ANY PURPOSE  EXCEPT AS  PROVIDED  ABOVE AND SHALL NOT BE
DEEMED TO CONFER RIGHTS ON ANY PERSON OTHER THAN THE PARTIES HERETO. EACH PARENT
HEREBY   WAIVES  ANY   OBJECTION  IT  MAY  HAVE  BASED  UPON  LACK  OF  PERSONAL
JURISDICTION, IMPROPER VENUE OR FORUM NON-CONVENIENS.

         4.16 Waiver of Jury Trial.  EACH PARTY  HEREBY KNOWINGLY AND INTENTION-
ALLY,  IRREVOCABLY AND UNCONDITIONALLY  WAIVES TRIAL BY JURY IN ANY LEGAL ACTION
OR PROCEEDING RELATING TO THIS AGREEMENT AND FOR ANY COUNTERCLAIM THEREIN.

         4.17 Dispute  Resolution.  All disputes under this  Agreement  shall be
resolved in  accordance  with the  Dispute  Resolution  Procedures  set forth in
Appendix B.

         4.18 Amendment. All waivers,  modifications,  amendments or alterations
of this Agreement shall require the execution of a written  instrument signed by
each of the parties hereto.






                            [signature page follows]






         IN WITNESS WHEREOF, the parties hereto have executed and delivered this
Parent Agreement as of the date first above written.


                                        LYONDELL PETROCHEMICAL COMPANY



                                        By:  /s/ Dan F. Smith
                                        Name:   Dan F. Smith
                                        Title:  President and Chief Executive
                                                Officer

                                        MILLENNIUM CHEMICALS INC.



                                        By:  /s/ George H. Hempstead, III
                                        Name:   George H. Hempstead, III
                                        Title:  Senior Vice President


                                        EQUISTAR CHEMICALS, LP



                                        By:  /s/ Debra L. Starnes
                                        Name:   Debra L. Starnes
                                        Title:  Senior Vice President






                                      

                                   APPENDIX A
                                       TO
                                PARENT AGREEMENT


                           LIST OF RELATED AGREEMENTS
                           --------------------------


        1.  Partnership Agreement

        2.  Lyondell Note (as such term is defined in the Partnership Agreement)

        3.  Asset Contribution Agreements

            a.  Among Lyondell, Lyondell LP and the Partnership

            b.  Among Millennium Petrochemicals Inc., Millennium LP and the 
                Partnership

        4.  [List here all agreements listed as Tier 2 Agreements in Master 
            Transaction Agreement]








                                       

                                   APPENDIX B
                                       TO
                                PARENT AGREEMENT

                          DISPUTE RESOLUTION PROCEDURES
                          -----------------------------


         (1) Binding and Exclusive Means. The dispute resolution  provisions set
forth in this Appendix B shall be the binding and exclusive means to resolve all
disputes arising under this Agreement (each a "Dispute").

         (2) Standards and Criteria. In resolving any Dispute, the standards and
criteria  for  resolving  such  dispute  shall,  unless  the  Parents  in  their
discretion  jointly stipulate  otherwise,  be as set forth in Appendix 1 to this
Appendix B.

         (3) ADR and Binding  Arbitration  Procedures.  If a Dispute arises, the
following procedures shall be implemented:

         (a) The Parent from whom  recovery is sought may at any time invoke the
dispute resolution  procedures set forth in this Appendix B as to any Dispute by
providing  written  notice of such action to the other  Parent,  who within five
Business Days after such notice shall  schedule a meeting to be held in Houston,
Texas between the Parents. The meeting shall occur within 10 Business Days after
notice of the meeting is delivered  to the other  Parent.  The meeting  shall be
attended by  representatives  of each Parent  having  decision-making  authority
regarding  the Dispute as well as the dispute  resolution  process and who shall
attempt in a  commercially  reasonable  manner to negotiate a resolution  of the
Dispute.

         (b)  The   representatives   of  the  Parents  shall   cooperate  in  a
commercially  reasonable  manner and shall explore  whether  techniques  such as
mediation,  minitrials,  mock trials or other techniques of alternative  dispute
resolution might be useful. In the event that a technique of alternative dispute
resolution is so agreed upon, a specific  timetable and completion  date for its
implementation  shall also be agreed upon. The representatives  will continue to
meet and discuss settlement until the date (the "Interim Decision Date") that is
the earliest to occur of the following events: (i) an agreement shall be reached
by the Parents  resolving the Dispute;  (ii) one of the Parents shall  determine
and notify the other Parent in writing that no agreement  resolving  the Dispute
is likely to be reached;  (iii) if a technique of alternative dispute resolution
is agreed upon,  the  completion  date therefor  shall occur without the Parents
having resolved the Dispute; or (iv) if another technique of alternative dispute
resolution is not agreed upon,  two full meeting days (or such other time period
as may be agreed  upon) shall  expire  without the Parents  having  resolved the
Dispute.

         (c) If, as of the Interim Decision Date, the Parents have not succeeded
in  negotiating  a resolution  of the dispute  pursuant to  subsection  (b), the
Parents shall proceed under subsection (d).

         (d) The Parents agree to appoint a mutually  acceptable  neutral person
not affiliated with any of the Parents (the "Neutral"). If the Parents have been
unable to agree upon such appointment  within 30 days after the Interim Decision
Date, then such Neutral,  upon the application of either of the Parents shall be
appointed  within 10 days of the  filing of such  application  by the Center for
Public  Resources,  or if such appointment is not so made promptly then promptly
thereafter   by  the   American   Arbitration   Association   in   Philadelphia,
Pennsylvania,  or if such  appointment  is not so made  promptly  then  promptly
thereafter  by  the  senior  United  States  District  Court  judge  sitting  in
Wilmington,  Delaware.  The fees of the  Neutral  shall be paid  equally  by the
Parents except that the Neutral shall have discretion to award fees.

         (e) In  consultation  with the Neutral,  the Parents shall agree upon a
binding  schedule  and  procedure  (which  procedure  may have  been  previously
discussed  under  subsection (b)) to be used as a means to resolve or to attempt
to resolve  Dispute,  with the Neutral  making the  decision as to the  schedule
and/or procedure if the Parents have been unable to agree on any of such matters
within 20 days after the initial selection of the Neutral.  The Parents agree to
participate  in a  commercially  reasonable  manner  in  the  procedure  to  its
conclusion as determined  by the Neutral.  If the Parents are not  successful in
resolving the Dispute through the procedure  described  above,  then the Parents
agree that (i) the Neutral shall act as the arbitrator in a binding  arbitration
in accordance with the American Arbitration Association rules and shall render a
decision  and (ii)  judgment  upon the  decision  rendered by the Neutral may be
entered in any court having jurisdiction.

         (4)  Continuation  of Business.  Notwithstanding  the  existence of any
Dispute or the  pendency  of any  procedures  pursuant  to this  Appendix B, the
Parents agree and undertake  that all payments not in dispute shall  continue to
be made and all obligations not in dispute shall continue to be performed.






                                   Appendix 1
                                   ----------


         (a) First priority shall be given to maximizing the  consistency of the
resolution of the Dispute with the  satisfaction  of all express  obligations of
the Parents and their Affiliates as set forth in the Agreement.

         (b) Second  priority  shall be given to  resolution of the Dispute in a
manner  which best  achieves  the  objectives  of the  business  activities  and
arrangements under the Agreement and permits the Parents to realize the benefits
intended to be afforded thereby.

         (c) Third priority shall be given to such other matters, if any, as the
Parents  or  the  Neutral   shall   determine  to  be   appropriate   under  the
circumstances.