Exhibit 10.10(b)

                            MILLENNIUM CHEMICALS INC.

                                  Amendment To

                     MILLENNIUM PETROCHEMICALS GRANDFATHERED
                     SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN

                                  (the "Plan")


         The Plan shall be, and it hereby is, amended effective June 1, 2002 as
follows:

1.       Section 11.3 Change in Control

         Amend clause (iv) of Section 11.3 to read in its entirety as follows:

         "(iv) the stockholders of the Company approve a plan of complete
         liquidation of the Company or the closing of the sale or disposition by
         the Company of all or substantially all of the Company's assets other
         than the sale or disposition of all or substantially all of the assets
         of the Company to one or more Subsidiaries (as defined below) of the
         Company or to a person or persons who beneficially own, directly or
         indirectly, at least fifty percent (50%) or more of the combined voting
         power of the outstanding voting securities of the Company at the time
         of the sale or disposition; provided, however, (y) the sale or
         disposition of all or any part of the Company's interests in Equistar
         Chemicals LLP ("Equistar") (and all subsequent sales and dispositions
         of any securities or assets received as proceeds thereof, or as
         proceeds of proceeds) shall not be deemed to constitute a Change in
         Control, and (z) if the Company sells or disposes of all or any part
         of the Company's interests in Equistar indirectly (either through the
         sale or other disposition of any entity that owns, directly or
         indirectly, all or any part of the Company's interests in Equistar, or
         otherwise), then the sale or disposition of the Company's interests in
         Equistar (and all subsequent sales and dispositions of any securities
         or assets received as proceeds thereof, or as proceeds of proceeds)
         shall be ignored and disregarded in determining whether any such Change
         in Control has occurred. By way of illustration, if an indirect
         subsidiary of the Company that owns the Company's interests in Equistar
         together with certain other assets is sold, then, in determining
         whether a Change in Control has occurred, all relevant determinations
         shall be made pursuant to the assumption that (y) such subsidiary owns
         only such other assets, and (z) neither such subsidiary nor the Company
         owns, either directly or indirectly, the interests in Equistar.
         "Subsidiary" shall have the meaning set forth in Section 424 of the
         Internal Revenue Code and the term shall also include any partnership,
         limited liability company or other business entity if the Company owns
         directly or indirectly, securities or other ownership interests
         representing at least fifty percent (50%) of the ordinary voting power
         or equity or capital interests of such entity."