<PAGE>

                                                                  Exhibit 4.5(c)



                          LYONDELL CHEMICAL COMPANY,

                            EQUISTAR CHEMICALS, LP

                                      and

                           THE CHASE MANHATTAN BANK,

                                    Trustee



                         THIRD SUPPLEMENTAL INDENTURE

                                  Dated as of

                               November 3, 2000

                                      to

                                   INDENTURE

                                  Dated as of

                               January 29, 1996

             (as supplemented by the First Supplemental Indenture
           dated as of February 15, 1996 and the Second Supplemental
                    Indenture dated as of December 1, 1997)
<PAGE>

          THIS THIRD SUPPLEMENTAL INDENTURE (this "Supplement"), dated as of
November 3, 2000 (the "Closing Date"), among Lyondell Chemical Company, a
Delaware corporation (formerly known as Lyondell Petrochemical Company,
"Lyondell"), Equistar Chemicals, LP, a Delaware limited partnership
("Equistar"), and The Chase Manhattan Bank, successor by merger to Chase Bank of
Texas, National Association (formerly known as Texas Commerce Bank National
Association), as Trustee (the "Trustee"), supplements the Indenture dated as of
January 29, 1996, between Lyondell and the Trustee under the Indenture, as
supplemented by the First Supplemental Indenture dated as of February 15, 1996
(the "First Supplemental Indenture"), pursuant to which the 6.50% Notes Due 2006
and 7.55% Debentures Due 2026 (collectively, the "Notes") were issued by
Lyondell and are outstanding, and the Second Supplemental Indenture dated as of
December 1, 1997 (the "Second Supplemental Indenture"), pursuant to which
Equistar became an obligor under the Indenture (such Indenture, as so amended
and supplemented, the "Indenture").

                                   RECITALS

          WHEREAS, Lyondell has executed and delivered to the Trustee the
Indenture, providing for the issuance from time to time of Lyondell's unsecured
debentures, notes or other evidences of indebtedness, issuable in one or more
series (the "Securities"), and Lyondell has executed and delivered to the
Trustee the First Supplemental Indenture, providing for the issuance of the
Notes, which are Securities under the Indenture;

          WHEREAS, Lyondell contributed substantially all of its assets (for
purposes of Section 12.01 of the Indenture) to Equistar effective December 1,
1997;

          WHEREAS, pursuant to the Asset Contribution Agreement dated as of
December 1, 1997, among Lyondell, Lyondell Petrochemical L.P. Inc. and Equistar,
Equistar assumed the Notes;

          WHEREAS, Section 11.01 of the Indenture provides that under certain
conditions, the Company and the Trustee may enter into an indenture or
indentures supplemental to the Indenture, inter alia, to evidence the succession
of another corporation to the Company and the assumption by any such successor,
pursuant to Article 12 of the Indenture of the covenants, agreements and
obligations of the Company contained in the Indenture and the Securities;

          WHEREAS, pursuant to Section 11.01(a) of the Indenture,  Lyondell,
Equistar and the Trustee entered into the Second Supplemental Indenture;

          WHEREAS, in accordance with Section 12.01 of the Indenture, pursuant
to the Second Supplemental Indenture, Equistar (a) expressly assumed the due and
punctual payment of the principal of and premium, if any, and interest, if any,
on all of the Securities of each series, according to their tenor, and the due
and punctual performance and observance of all of the covenants and conditions
of the Indenture, as supplemented by the First and Second Supplemental
Indentures, and in such series to be performed by Lyondell; and (b) succeeded to
and was substituted for Lyondell as the "Company" for purposes of the Indenture,
with the same effect as if Equistar had been named as the "Company" in the
Indenture, as supplemented;
<PAGE>

          WHEREAS, the Second Supplemental Indenture provided that subsequent to
December 1, 1997, for purposes of the Indenture, the term "Company" shall mean
and include both Equistar and Lyondell, and Equistar shall not be a "Subsidiary"
of Lyondell;

          WHEREAS, Section 11.01(b) of the Indenture provides that, without the
consent of any Holders of any series of Securities, the Company and the Trustee
may enter into an indenture or indentures supplemental to the Indenture, inter
alia, to add to the covenants of the Company such further covenants,
restrictions or conditions for the protection of the Holders of any series of
Securities as the Board of Directors and the Trustee shall consider to be for
the protection of the Holders of such Securities;

          WHEREAS, Section 11.01(h) of the Indenture provides that, without the
consent of any Holders of any series of Securities, the Company and the Trustee
may enter into an indenture or indentures supplemental to the Indenture to
conform the Indenture to the provisions of the Trust Indenture Act of 1939 (the
"TIA");

          WHEREAS, Lyondell and Equistar have duly determined to make, execute
and deliver to the Trustee this Supplement pursuant to Section 11.01 of the
Indenture, in order to (1) provide for the Guarantee, as hereinafter defined, of
the payment of the Notes, by Lyondell as the Guarantor, as hereinafter defined,
under the Indenture, and (2) amend certain provisions of the Indenture to
conform to the provisions of the TIA.

          NOW, THEREFORE, THIS SUPPLEMENT WITNESSETH:

          In consideration of the premises and other good and valuable
consideration, the parties hereto hereby agree, for the equal and proportionate
benefit of the respective Holders from time to time of the Securities, as
follows:

                                  SECTION ONE

                                  DEFINITIONS

          Capitalized terms used and not otherwise defined herein have the
respective meanings assigned to such terms in the Indenture.

                                      -3-
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                                  SECTION TWO

                                  AMENDMENTS

     2.1  Section 1.01 of the Indenture shall be amended to add the following
          definitions:

          Guarantee

          The term "Guarantee" shall mean the guarantee by the Guarantor of the
          Company's obligations provided for by the third supplemental indenture
          to the Indenture.

          Guarantor

          The term "Guarantor" shall mean Lyondell Chemical Company, a Delaware
          corporation, until such time as Lyondell Chemical Company is released
          from its Guarantee as permitted by the Indenture.

          obligor

          The term "obligor" shall mean the Company, the Guarantor or any other
          obligor on the Securities.

          United States Bankruptcy Code

          The term "United Stated Bankruptcy Code" shall mean Title 11 of the
          United States Code, Section 101 et seq.

     2.2  Section 5.08 of the Indenture shall be amended so that (a) the first
          reference to  "The Company" is changed to "Each obligor" and (b) all
          subsequent references to "the Company" are changed to "such obligor".

     2.3  Section 6.01 of the Indenture shall be amended so that (a) the first
          reference to "The Company" is changed to "Each obligor under the
          Securities" and (b) the second reference to "the Company" is changed
          to "such obligor".

     2.4  Section 6.02(c) of the Indenture shall be amended so that (a) the
          first reference to "the Company" is changed to "each obligor" and (b)
          the second reference to "the Company" is changed to "such obligor".

     2.5  Section 6.03(a) of the Indenture shall be amended so that (a) the
          section caption "Reports by the Company" is changed to "Reports by
          each obligor", (b) the first reference to "The Company" is changed to
          "Each obligor", and (c) all subsequent references to "the Company" are
          changed to "such obligor".

                                      -4-
<PAGE>

     2.6  Section 6.03(b) of the Indenture shall be amended so that (a) the
          first reference to "The Company" is changed to "Each obligor" and (b)
          the second reference to "the Company" is changed to "such obligor".

     2.7   Section 6.03(c) of the Indenture shall be amended so that (a) the
           first reference to "The Company" is changed to "Each obligor" and (b)
           the second reference to "the Company" is changed to "such obligor".

     2.8   Section 6.04(c)(1) of the Indenture shall be amended so that the
           reference to "the Company" is changed to "each obligor".

     2.9   Section 7.01(d) of the Indenture shall be amended so that (a) the
           first, third and fourth references to "the Company" are changed to
           "the Company or the Guarantor, as applicable," and (b) the second
           reference to "the Company" is changed to "the Company or the
           Guarantor".

     2.10  Section 7.01(g) of the Indenture shall be amended so that the
           reference to "if any." is replaced with "if any; or".

     2.11  Section 7.01 of the Indenture shall be amended by inserting the
           following paragraph:

           (h) except as permitted by the Indenture, the Guarantee issued under
           the Indenture shall be held in any judicial proceeding to be
           unenforceable or invalid or shall cease for any reason to be in full
           force and effect or the Guarantor, or any Person acting on behalf of
           the Guarantor, shall deny or disaffirm its obligations under the
           Guarantee issued under the Indenture.

     2.12  Section 7.07 of the Indenture shall be amended so that the reference
           to "the Company" is changed to "the Company, the Guarantor".

     2.13  Section 8.08 of the Indenture shall be amended so that the reference
           to "the Company" is changed to "any obligor".

     2.14  Section 8.09(b) of the Indenture shall be amended so that (a) the
           first reference to "the Company" is changed to "any obligor" and (b)
           the second reference to "the Company" is changed to "such obligor".

     2.15  Section 9.03 of the Indenture shall be amended so that (a) the first
           reference to "The Company" is changed to "The Company, the Guarantor"
           and (b) the third reference to "the Company" is changed to "the
           Company nor the Guarantor".

     2.16  Section 9.05(b) of the Indenture shall be amended so that the
           reference to "or the Company" is changed to ", the Company or the
           Guarantor".

                                      -5-
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     2.17  Section 11.01(a) of the Indenture shall be amended so that the
           following paragraph is added to the end of the paragraph:

           or to evidence the succession of another corporation to the
           Guarantor, or successive successions, and the assumption by the
           successor corporation, pursuant to Section Four of the third
           supplemental indenture to the Indenture, of the covenants, agreements
           and obligations of the Guarantor in the Indenture and in the
           Securities contained;

     2.18  The first paragraph of Section 11.02 of the Indenture shall be
           amended so that the following is added to the end of the first
           sentence thereof:

           or (iv) modify or change any provision of the Indenture affecting the
           ranking of the Guarantee in a manner adverse to the Holders of the
           Securities, or (v) release the Guarantor from any of its obligations
           under the Guarantee or the Indenture other than in accordance with
           the provisions of the Indenture, or amend or modify any provision
           relating to such release.

     2.19  Section 11.03 of the Indenture shall be amended so that the reference
           to "the Company" is changed to "the Company, the Guarantor".

     2.20  The first paragraph of Section 14.02 of the Indenture shall be
           amended so that the following is added after the first reference to
           "Securities of any series":

           (and any Guarantor will be discharged from any and all obligations in
           respect of its Guarantee)

     2.21  Section 15.01 of the Indenture shall be amended so that the
           references to "the Company" are changed to "the Company or the
           Guarantor".

     2.22  Section 16.01 of the Indenture shall be amended so that (a) the
           section caption "Provisions Binding on Company's Successors" is
           changed to "Provisions Binding on Successors", (b) the reference to
           "the Company" is changed to "the Company and the Guarantor", and (c)
           the reference to "its" is changed to "their respective".

     2.23  Section 16.03 of the Indenture shall be amended so that (a) the first
           reference to "the Company" is changed to "the Company or the
           Guarantor" and (b) the last reference to "the Company" is changed to
           "the Company or the Guarantor, as applicable".

                                      -6-
<PAGE>

                                 SECTION THREE

                                   GUARANTEE

     3.1  The Guarantee.  Subject to the provisions of this Section Three, the
          Guarantor hereby irrevocably and unconditionally guarantees the full
          and punctual payment (whether at Stated Maturity, upon acceleration,
          optional redemption or otherwise) of the principal of and premium, if
          any, and interest on, and all other amounts payable under, each of the
          Securities provided for under the Indenture, and the full and punctual
          payment of all other amounts payable by the Company under the
          Indenture.  Upon failure by the Company to pay punctually any such
          amount, the Guarantor shall forthwith on demand pay the amount not so
          paid at the place and in the manner specified in the Indenture.

     3.2  Guarantee Unconditional.  The obligations of the Guarantor hereunder
          shall be unconditional and absolute and, without limiting the
          generality of the foregoing, shall, to the fullest extent permitted by
          law, not be released, discharged or otherwise affected by:

          (a)  any extension, renewal, settlement, compromise, waiver or release
          in respect of any obligation of the Company under the Indenture or any
          Security, by operation of law or otherwise;

          (b)  any modification or amendment of or supplement to the Indenture
          or any Security; provided that any such modification which increases
          the obligations of the Guarantor hereunder shall not be effective as
          to the Guarantor without its consent;

          (c)  any release, impairment, non-perfection or invalidity of any
          direct or indirect security for any obligation of the Company or the
          Guarantor hereunder;

          (d)  any change in the corporate existence, structure or ownership of
          the Company, or any insolvency, bankruptcy, reorganization or other
          similar proceeding affecting the Company or its assets or any
          resulting release or discharge of any obligation of the Company
          contained in the Indenture or any Security;

          (e)  the existence of any claim, set-off or other rights which the
          Guarantor may have at any time against the Company, the Trustee or any
          other Person, whether in connection with the Indenture or any
          unrelated transactions, provided that nothing herein shall prevent the
          assertion of any such claim by separate suit or compulsory
          counterclaim;

          (f)  any invalidity or unenforceability relating to or against the
          Company for any reason of the Indenture or any Security, or any
          provision of applicable law or

                                      -7-
<PAGE>

          regulation purporting to prohibit the payment by the Company of the
          principal of or interest on any Security or any other amount payable
          by the Company under the Indenture; or

          (g)  any other act or omission to act or delay of any kind by the
          Company, the Trustee or any other Person or any other circumstance
          whatsoever which might, but for the provisions of this paragraph,
          constitute a legal or equitable discharge of or defense to the
          Guarantor's obligations hereunder.

     3.3  Discharge; Reinstatement.  The Guarantor's obligations hereunder shall
          remain in full force and effect until the principal of, premium, if
          any, and interest on the Securities and all other amounts payable by
          the Company under the Indenture shall have been paid in full.  If at
          any time any payment of the principal of, premium, if any, or interest
          on any Security or any other amount payable by the Company under the
          Indenture is rescinded or must be otherwise restored or returned upon
          the insolvency, bankruptcy or reorganization of the Company or
          otherwise, the Guarantor's obligations hereunder with respect to such
          payment shall be reinstated as though such payment had been due but
          not made at such time.

     3.4  Waiver by the Guarantor.  The Guarantee is a guarantee of payment and
          not of collection.  The Guarantor irrevocably waives acceptance
          hereof, presentment, demand, protest and any notice not provided for
          herein, as well as any requirement that at any time any action be
          taken by any Person against the Company or any other Person.

     3.5  Subrogation and Contribution. Upon making any payment with respect to
          any obligation of the Company under this Section Three, the Guarantor
          making such payment shall be subrogated to the rights of the payee
          against the Company with respect to such obligation; provided that the
          Guarantor shall not enforce any right to receive payment by way of
          subrogation against the Company or against any direct or indirect
          security for such obligation, or any other right to be reimbursed,
          indemnified or exonerated by or for the account of the Company in
          respect thereof, so long as any amount payable by the Company under
          the Indenture or under the Securities remains unpaid.

     3.6  Stay of Acceleration.  If acceleration of the time for payment of any
          amount payable by the Company under the Indenture or the Securities is
          stayed upon the insolvency, bankruptcy or reorganization of the
          Company, all such amounts otherwise subject to acceleration under the
          terms of the Indenture shall nonetheless be payable by the Guarantor
          hereunder forthwith on demand by the Trustee or the Holders.

     3.7  Limits of Guarantee.  Notwithstanding anything to the contrary in this
          Section Three, it is the intention that the Guarantee not constitute a
          fraudulent  conveyance under

                                      -8-
<PAGE>

          applicable fraudulent conveyance provisions of the United States
          Bankruptcy Code or any comparable provision of state law. To
          effectuate the foregoing intention, the Trustee, and the Guarantor
          hereby irrevocably agree that the obligations of the Guarantor under
          the Guarantee and this Section Three shall be limited to the maximum
          amount that would not render the Guarantor's obligations subject to
          avoidance under applicable fraudulent conveyance provisions of the
          United States Bankruptcy Code or any comparable provision of state
          law.

     3.8  Subsequent Delivery of Securities Guarantee.  The delivery of any
          Security by the Trustee, after the authentication thereof hereunder,
          shall constitute due delivery of the Guarantee set forth in this
          Supplement on behalf of the Guarantor.

     3.9  Notwithstanding any of the provisions of Section Three or any release
          subsequent hereto of the Guarantor as "the Company" or otherwise as a
          primary obligor under the Indenture and the Securities, the Guarantor,
          in its capacity as such, retains and  does not hereby waive or
          surrender any defenses or rights it has or would have in its capacity
          as the issuer of the Securities.

                                 SECTION FOUR

                CONSOLIDATION, MERGER AND SALE BY THE GUARANTOR

     4.1  Guarantor may Consolidate, etc., on Certain Terms.  Subject to any
          modification contained in any indenture supplemental hereto under
          which any series of Securities is issued and subject to the provisions
          of Section 12.02 of the Indenture, nothing contained in the Indenture
          or in any of the Securities shall prevent any consolidation or merger
          of the Guarantor with or into any other  corporation or corporations
          (whether or not affiliated with the Guarantor), or successive
          consolidations or mergers in which the Guarantor or its successor or
          successors shall be a party or parties, or shall prevent any sale or
          conveyance of all or substantially all the property of the Guarantor,
          to party or parties, or shall prevent any sale or conveyance of all or
          substantially all the property of the Guarantor, to any other
          corporation (whether or not affiliated with the Guarantor) authorized
          to acquire and operate the same; provided however, that upon any such
          consolidation, merger, sale or conveyance, other than a consolidation
          or merger in which the Guarantor is the continuing corporation, the
          Guarantee and the observance of all of the covenants and conditions of
          the Indenture and in such series to be performed by the Guarantor,
          shall be expressly assumed, by supplemental indenture satisfactory in
          form to the Trustee, executed and delivered to the Trustee by the
          corporation (if other than the Guarantor) formed by such
          consolidation, or into which the Guarantor shall have been merged, or
          by the corporation which shall have acquired such property; and
          provided further that the Guarantor or such successor corporation, as
          the case may be, shall not immediately after such merger,
          consolidation, or such sale or conveyance, be in default in the
          performance of any such covenant or condition.

                                      -9-
<PAGE>

     4.2  Successor Corporation to be Substituted.  In case of any such
          consolidation, merger, sale or conveyance and upon the assumption by
          the successor corporation, by supplemental indenture, executed and
          delivered to the Trustee and satisfactory in form to the Trustee, of
          the Guarantee and the due and punctual performance of all of the
          covenants and conditions of the Indenture to be performed by the
          Guarantor, such successor corporation shall succeed to and be
          substituted for the Guarantor, with the same effect as if it had been
          named herein and, if the Guarantor is to be voluntarily dissolved, the
          Guarantor shall thereupon be released from all obligations under the
          Indenture and under the Securities.

     4.3  Opinion of Counsel to be Given Trustee.  Before the Trustee shall
          execute any supplemental indenture required pursuant to this Section
          Four, the Trustee, subject to Sections 8.01 and 8.02 of the Indenture,
          shall receive and shall be fully protected in relying upon, an
          Officers' Certificate and an Opinion of Counsel as conclusive evidence
          that any such consolidation, merger, sale or conveyance and any such
          assumption complies with the provisions of this Section.

                                 SECTION FIVE

                                 RATIFICATION

          Except as expressly amended and supplemented on this Supplement, the
Indenture shall remain unchanged and in full force and effect.  This Supplement
shall be construed as supplemental to the Indenture and shall form a part
thereof.

                                  SECTION SIX

                                 GOVERNING LAW

          This Supplement shall be governed by and construed in accordance with
the laws of the State of New York applicable to agreements made and to be
performed therein.

                                 SECTION SEVEN

                                 COUNTERPARTS

          This instrument may be executed in any number of counterparts, each of
which so executed shall be deemed to be an original, but all such counterparts
shall together constitute but one and the same instrument.

                                      -10-
<PAGE>

          IN WITNESS WHEREOF, each of Lyondell Chemical Company and Equistar
Chemicals, LP have caused this Third Supplemental Indenture to be duly executed
and The Chase Manhattan Bank as Trustee, has caused this Third Supplemental
Indenture to be signed by one of its Vice Presidents or Assistant Vice
Presidents as of the day and year first above written.


                              LYONDELL CHEMICAL COMPANY


                              By /s/ Robert T. Blakely
                                 ---------------------------------------
                                    Robert T. Blakely
                                    Executive Vice President and
                                    Chief Financial Officer



                              EQUISTAR CHEMICALS, LP


                              By /s/ Eugene R. Allspach
                                 ---------------------------------------
                                    Eugene R. Allspach
                                    President and Chief Operating Officer



                              THE CHASE MANHATTAN BANK
                              Trustee


                              By /s/ Mauri J. Cowen
                                 ---------------------------------------
                                    Name:  Mauri J. Cowen
                                    Title: Vice President and Trust Officer

                                      -11-