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                                                                    EXHIBIT 4(b)



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                            ANADARKO FINANCE COMPANY
                                                      , AS COMPANY

                         ANADARKO PETROLEUM CORPORATION
                                                          , AS GUARANTOR

                                       AND

                              THE BANK OF NEW YORK
                                                   , AS TRUSTEE

                                   ----------

                          FIRST SUPPLEMENTAL INDENTURE

                           DATED AS OF MAY 23, 2001 TO

                                    INDENTURE

                           DATED AS OF APRIL 26, 2001




                                  $550,000,000
          ADDITIONAL 6 3/4% SERIES A AND SERIES B SENIOR NOTES DUE 2011


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                          FIRST SUPPLEMENTAL INDENTURE

         This FIRST SUPPLEMENTAL INDENTURE, dated as of May 23, 2001 (this
"First Supplemental Indenture"), to the Indenture, dated as of April 26, 2001
(the "Indenture"), is by and among Anadarko Finance Company, an unlimited
liability company organized under the laws of the province of Nova Scotia,
Canada (the "Company"), Anadarko Petroleum Corporation, a Delaware corporation
(the "Guarantor"), and The Bank of New York, as trustee (the "Trustee").

                            RECITALS OF THE COMPANY:

         WHEREAS, pursuant to the Indenture the Company established and provided
for the issuance by the Company of four series of Securities, of which (i) two
series are designated as the 6 3/4% Series A Senior Notes due 2011 (the "10-Year
Series A Securities") and the 6 3/4% Series B Senior Notes due 2011 (the
"10-Year Series B Securities" and, collectively with the 10-Year Series A
Securities, the "10-Year Securities") and (ii) each such series is in the
aggregate principal amount of $400,000,000 and unconditionally guaranteed by the
Guarantor;

         WHEREAS, Section 2.02 of the Indenture expressly provides that any
additional amount of Securities may be issued and authenticated upon a written
order of the Company specifying (a) the amount of Securities of each series to
be authenticated and the date of original issue thereof, and (b) whether the
Securities are Series A Securities or Series B Securities;

         WHEREAS, the Company desires to reopen the 10-Year Securities and issue
$550,000,000 principal amount of additional 10-Year Series A Securities and,
pursuant to an Exchange Offer or Private Exchange, $550,000,000 principal amount
of 10-Year Series B Securities, which will be part of the same series as the
10-Year Series A Securities and 10-Year Series B Securities, respectively,
issued on the Issue Date, and will rank equally with such 10-Year Series A
Securities and 10-Year Series B Securities, respectively, in all respects;

         WHEREAS, the Guarantor has agreed to unconditionally guarantee the
additional 10-Year Securities in accordance with Article IX of the Indenture;

         WHEREAS, the conditions set forth in the Indenture for the execution
and delivery of this First Supplemental Indenture have been complied with; and

         WHEREAS, all things necessary to make this First Supplemental Indenture
a valid and binding agreement of the Company, the Guarantor and the Trustee, in
accordance with its terms, and a valid and binding amendment of, and supplement
to, the Indenture have been done;

         NOW THEREFORE:

         Pursuant to Section 2.02 of the Indenture, the 10-Year Securities
established by the Indenture is hereby reopened and there is hereby authorized
for issuance, authentication and delivery $550,000,000 principal amount of
10-Year Series A Securities (the "Additional 10-Year Series A Securities") and,
for original issue pursuant to an Exchange Offer or Private Exchange for a like
principal amount of the 10-Year Series A Securities, $550,000,000 principal
amount of 10-Year Series B Securities (the "Additional 10-Year Series B
Securities" and, collectively with the Additional 10-Year Series A Securities,
the "Additional 10-Year Securities"), such Additional 10-Year Series A
Securities and Additional 10-Year Series B Securities to be of the same series
as the 10-Year Series A Securities and 10-Year Series B Securities,
respectively, and



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in consideration of the premises and the purchase and acceptance of the
Additional 10-Year Securities by the Holders thereof, the Company and the
Guarantor mutually covenant and agree with the Trustee, for the equal and
proportionate benefit of all Holders of the 10-Year Securities and the
Additional 10-Year Securities, that the Indenture is hereby supplemented and
amended, to the extent and for the purposes expressed herein, as follows:

                                   ARTICLE ONE
                           AMENDMENTS TO THE INDENTURE

         Section 1.1 Amendments to Indenture. The Indenture is hereby amended
and supplemented as follows:

                  (a) The 10-Year Series A Securities established by the
         Indenture is hereby reopened for the issuance of Additional 10-Year
         Series A Securities in an aggregate principal amount of $550,000,000
         which shall rank equally with the 10-Year Series A Securities in all
         respects, shall form a single series of $950,000,000 aggregate
         principal amount with the 10-Year Series A Securities, with the same
         CUSIP number, and shall have the same terms as the 10-Year Series A
         Securities, except that the date of original issuance of the Additional
         10-Year Series A Securities will be May 23, 2001. The 10-Year Series B
         Securities established by the Indenture which are to be issued pursuant
         to an Exchange Offer or Private Exchange for a like principal amount of
         10-Year Series A Securities is hereby reopened for the original issue,
         pursuant to an Exchange Offer or Private Exchange, of $550,000,000
         Additional 10-Year Series B Securities for a like principal amount of
         10-Year Series A Securities, which Additional 10-Year Series B
         Securities shall rank equally with the 10-Year Series B Securities in
         all respects, shall form a single series of $950,000,000 aggregate
         principal amount of the 10-Year Series B Securities, with the same
         CUSIP number, and shall have the same terms as the 10-Year Series B
         Securities. Interest on the Additional 10-Year Securities shall accrue
         from April 26, 2001. The form of Additional 10-Year Securities to be
         issued shall be identical to the form of 10-Year Securities included as
         Exhibit A to the Indenture, except that the date of original issuance
         of the Additional 10-Year Series A Securities will be May 23, 2001 and
         references therein to the Registration Rights Agreement dated as of
         April 26, 2001 shall instead refer to the Registration Rights Agreement
         dated as of May 23, 2001.

                  (b) All references in the Indenture and the form of 10-Year
         Securities attached thereto as Exhibit A to the 10-Year Securities
         established by the Indenture and in the outstanding 10-Year Securities
         shall be amended, supplemented and deemed to include the Additional
         10-Year Securities issued or authorized for issuance hereunder.

                  (c) The Additional 10-Year Securities shall be subject to the
         Indenture, as amended hereby.

                  (d) The following shall be added as Section 2.07(f) of the
         Indenture:

                           (f) In the event of a transfer, substitution or
                  replacement of a Global Security or certificated Security in
                  either case that is a Transfer Restricted Security, which
                  transfer, substitution or replacement occurs prior to
                  completion of the Exchange Offer, the Transfer Restricted
                  Security issued upon such transfer, substitution or
                  replacement shall contain in paragraph 18 thereof the
                  reference to the same Registration Rights Agreement referenced
                  in the Transfer Restricted



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                  Security in exchange, substitution or replacement for which
                  such new Transfer Restricted Security is being issued.

                                   ARTICLE TWO
                                  MISCELLANEOUS

         Section 2.1 Execution as Supplemental Indenture; Definitions. This
First Supplemental Indenture is executed and shall be construed as an indenture
supplemental to the Indenture and, as provided in the Indenture, this First
Supplemental Indenture forms a part thereof. Unless otherwise provided in this
First Supplemental Indenture, all defined terms used in this First Supplemental
Indenture shall have the respective meanings assigned to them in the Indenture.

         Section 2.2 Conflict of any Provision of Indenture with Trust Indenture
Act of 1939. If and to the extent that any provision of this First Supplemental
Indenture limits, qualifies or conflicts with another provision included in this
First Supplemental Indenture or in the Indenture which is required to be
included herein or therein by any of Sections 310 to 317, inclusive, of the
Trust Indenture Act of 1939, as amended, such required provision shall control.

         Section 2.3 New York Law to Govern. This First Supplemental Indenture
and the Securities (including the Additional 10-Year Securities) shall be
governed by and construed in accordance with the laws of the State of New York.

         Section 2.4 Counterparts. This First Supplemental Indenture may be
executed in any number of counterparts, each of which shall be an original, but
such counterparts shall together constitute but one and the same instrument.

         Section 2.5 Effect of Headings. The Article and Section headings herein
are for convenience only and shall not affect the construction hereof.

         Section 2.6 Severability of Provisions. In case any provision in this
First Supplemental Indenture or in the Securities (including the Additional
Securities) shall be invalid, illegal or unenforceable, the validity, legality
and enforceability of the remaining provisions shall not in any way be affected
or impaired thereby.

         Section 2.7 Successors and Assigns. All covenants and agreements in
this First Supplemental Indenture by the parties hereto shall bind their
respective successors and assigns and inure to the benefit of their respective
successors and assigns, regardless of whether so expressed.

         Section 2.8 Benefit of First Supplemental Indenture. Nothing in this
First Supplemental Indenture, express or implied, shall give to any Person,
other than the parties hereto, any Registrar, any Paying Agent and their
successors hereunder, and the Holders of the Securities, any benefit or any
legal or equitable right, remedy or claim under this First Supplemental
Indenture.

         Section 2.9 Acceptance by Trustee. The Trustee accepts the amendments
to the Indenture effected by this First Supplemental Indenture and agrees to
execute the trusts created by the Indenture as hereby amended, but only upon the
terms and conditions set forth in the Indenture. Without limiting the generality
of the foregoing, the Trustee assumes no responsibility for the correctness of
the recitals contained herein, which shall be taken as the



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statements of the Company and, except as provided in the Indenture, the Trustee
shall not be responsible or accountable in any way whatsoever for or with
respect to the validity or execution or sufficiency of this First Supplemental
Indenture and the Trustee makes no representation with respect thereto.

         IN WITNESS WHEREOF, the parties hereto have caused this First
Supplemental Indenture to be duly executed, all as of the date first above
written.

                                        Company:

                                        ANADARKO FINANCE COMPANY


                                        By:       /s/ ALBERT L. RICHEY
                                            ------------------------------------
                                            Name: A. L. Richey
                                            Title: Vice President and Treasurer


                                        Guarantor:

                                        ANADARKO PETROLEUM CORPORATION


                                        By:       /s/ ALBERT L. RICHEY
                                            ------------------------------------
                                            Name: A. L. Richey
                                            Title: Vice President and Treasurer


                                        Trustee:

                                        THE BANK OF NEW YORK


                                        By:       /s/ BEATA HRYNIEWICKA
                                            ------------------------------------
                                            Name: Beata Hryniewicka
                                            Title: Assistant Treasurer


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