EXHIBIT 99.3
 
                       NOTICE OF GUARANTEED DELIVERY FOR
 
    OFFER TO EXCHANGE NEWLY ISSUED         OFFER TO EXCHANGE NEWLY ISSUED
 
 
       4.90% EXCHANGEABLE SENIOR              4.95% EXCHANGEABLE SENIOR
          DEBENTURES DUE 2008                    DEBENTURES DUE 2008
 
                  OF                                     OF
 
           PENNZOIL COMPANY                       PENNZOIL COMPANY
 
     FOR A PORTION OF OUTSTANDING           FOR A PORTION OF OUTSTANDING
 
      6 1/2% EXCHANGEABLE SENIOR             4 3/4% EXCHANGEABLE SENIOR
          DEBENTURES DUE 2003                    DEBENTURES DUE 2003
 
 
 
  Registered holders of 6 1/2% exchangeable senior debentures due 2003 (the "6
1/2% Debentures") of Pennzoil Company, a Delaware corporation (the "Company"
or "Pennzoil") who wish to tender any such 6 1/2% Debentures in exchange for
new 4.90% exchangeable senior debentures due 2008 of the Company (the "New
4.90% Debentures") and registered holders of 4 3/4% exchangeable senior
debentures due 2003 (the "4 3/4% Debentures" and, together with the 6 1/2%
Debentures, the "Old Debentures"), who wish to tender any such 4 3/4%
Debentures in exchange for new 4.95% exchangeable senior debentures due 2008
(the "New 4.95% Debentures") of the Company, on the terms and subject to the
conditions set forth in the Prospectus of the Company, dated July 1, 1998 (the
"Prospectus"), and the related Letters of Transmittal, and whose Old
Debentures are not immediately available or who cannot deliver their Old
Debentures and the respective Letters of Transmittal (and any other documents
required by the Letters of Transmittal) to Chase Bank of Texas, National
Association (the "Exchange Agent") prior to the Expiration Dates (as defined
in the Prospectus), may use this Notice of Guaranteed Delivery or one
substantially equivalent hereto. This Notice of Guaranteed Delivery may be
delivered by hand or sent by facsimile transmission (receipt confirmed by
telephone and an original delivered by guaranteed overnight delivery) or
mailed to the Exchange Agent. See "The Exchange Offers--Procedures for
Tendering" in the Prospectus.
 
                  THE EXCHANGE AGENT FOR THE EXCHANGE OFFER:
 
                   CHASE BANK OF TEXAS NATIONAL ASSOCIATION
 
         By Hand or Overnight                               By Mail:
               Courier:                             (registered or certified
  c/o Chase Bank of     Chase Texas Trust Company       mail recommended)
       Texas,            55 Water Street, North         Chase Bank of Texas, 
National Association,           Building                National Association,
  Corporate Trust       Room 234, Windows 20 & 21     Corporate Trust Services
  Service  or           New York, New York 10041            P.O. Box 2320    
 1201 Main, 18th Floor                                Dallas, Texas 75221-2320
  Dallas, Texas 75202 
                      
                                Facsimile Number:
                       (For Eligible Institutions Only)
 
                                (214) 672-5746
 
                             Confirm by Telephone:
 
                                (214) 672-5678
 
  Delivery of this Notice of Guaranteed Delivery to an address other than as
set forth above or transmission of instructions via a facsimile transmission
to a number other than as set forth above will not constitute a valid
delivery.
 
  This Notice of Guaranteed Delivery is not to be used to guarantee
signatures. If a signature on a Letter of Transmittal is required to be
guaranteed by an Eligible Institution, such signature guarantee must appear in
the applicable space provided in the Letters of Transmittal for the guarantee
of signatures.

 
  The undersigned hereby tenders the aggregate principal amount at maturity of
Old Debentures indicated below, upon the terms and subject to the conditions
contained in the Prospectus, dated July 1, 1998, of the Company, receipt of
which is hereby acknowledged.
 
                    DESCRIPTION OF OLD DEBENTURES TENDERED
 
Aggregate Principal Amount at Maturity of 6 1/2% Debentures:$
 
Aggregate Principal Amount at Maturity of 4 3/4% Debentures:$
 
Certificate Number(s) (if available): ___________________
                          -------------------------------
 
  Unless otherwise indicated, the undersigned will be deemed to have tendered
the entire aggregate principal amount at maturity of Old Debentures held for
the account of the undersigned.
 
Address(es):_____________________________________________
     ------------------------------------------------
 
Area Code and Telephone Number: _________________________
 
Signature(s):____________________________________________
     ------------------------------------------------
 
If Old Debentures will be delivered by book-
entry transfer to The Depository Trust
Company, provide account number.
 
Account Number:_________________________________________
 
The undersigned has a net long position in Old Debentures or equivalent
securities at least equal to the Old Debentures described above (that will be
delivered within three New York Stock Exchange, Inc. trading days after the
date of execution of this Notice of Guaranteed Delivery) within the meaning of
Rule 14e-4 under the Securities Exchange Act of 1934, as amended.
 
                                       2

 
                   THE FOLLOWING GUARANTEE MUST BE COMPLETED
 
                             GUARANTEE OF DELIVERY
                   (NOT TO BE USED FOR SIGNATURE GUARANTEE)
 
  The undersigned, a firm that is a member of a registered national securities
exchange or a member of the National Association of Securities Dealers, Inc.
or a commercial bank or trust company having an office, branch, agency, or
correspondent in the United States, hereby guarantees to deliver to the
Exchange Agent at one of its addresses set forth above, the certificates
representing the Old Debentures, together with a properly completed and duly
executed Letter of Transmittal (or facsimile thereof), with any required
signature guarantees, and any other documents required by the Letter of
Transmittal, within three New York Stock Exchange, Inc. trading days after the
date of execution of this Notice of Guaranteed Delivery.
 
Name of Firm:________________________     -------------------------------------
Address:_____________________________            (Authorized Signature)
    -------------------------------       -------------------------------------
    -------------------------------       Name: _______________________________
          (Include Zip Code)                       (Please type or print)
Area Code and Telephone Number: _____     Title: ______________________________
Date: _______________________________
 
  NOTE: DO NOT SEND CERTIFICATES OF OLD DEBENTURES WITH THIS NOTICE OF
GUARANTEED DELIVERY. CERTIFICATES OF OLD DEBENTURES SHOULD BE SENT WITH YOUR
LETTERS OF TRANSMITTAL.
 
                                       3