Document:

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                                                                 Exhibit 10.2(a)

                            EQUISTAR CHEMICALS, LP
                                  BONUS PLAN

              (As Amended and Restated Effective January 1, 2000)

          Equistar Chemicals, LP (the "Company") has established a Bonus Plan
(the "Plan"), and hereby amends and restates the Plan effective as of January 1,
2000, in order to:

     .    Focus Participants on key measures of value creation for the Company's
          partners and on operating measures that lead to the creation of value.

     .    Provide significant upside and downside award potential commensurate
          with Company value creation.

     .    Encourage a long-term management perspective and reward for sustained
          long-term performance.

     .    Enhance the ability of the Company to attract and retain highly
          talented and competent individuals.

     .    Reinforce a team orientation among top management.

The Plan, as hereby amended and restated, shall apply to all payments made after
January 1, 2000, with respect to Awards granted prior to or after that date.

          1.   Definitions

          Award:  The amount payable under this Plan as determined by the
          -----
     Committee according to the performance of the Company during the Plan Year.

          Award Percentage:  The percentage of the Participant's Base Salary
          ----------------
     payable as a result of the Company's performance during the Plan Year,
     calculated in accordance with Section 7(a).

          Base Salary.  A Participant's annual base salary in effect on the last
          -----------
     day of the Plan Year.

          Committee: means the Compensation Committee of the Company's
          ---------
     Partnership Governance Committee.

          Disability: A permanent and total disability as defined in the
          ----------
     Company's Long-Term Disability Plan, if any, in which the Employee
     participates.
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          EBITDA: The Company's Earnings for the Plan Year before interest,
          ------
     taxes, depreciation and amortization.

          EVA:  EVA is the economic value added as measured by the Company's
          ---
     cash flow relative to the return that debt and equity holders expect to
     receive on the Company's capital.  Annual EVA is the difference between (i)
     cash generated by Company operations and (ii) the sum of the Company's debt
     and equity capital, multiplied by a factor representing investors' expected
     rate of return on that capital, as calculated under the formula in Schedule
     A.

          Financial Measures:  EVA, EBITDA and other objective measures of the
          ------------------
     Company's financial and operational performance utilized by the Committee
     to evaluate the Company's performance over the Plan Year.

          Participant:  An Employee selected by the Committee to receive an
          -----------
     opportunity to earn an Award pursuant to the Plan.

          Performance Percentage:  The percentage designated by the Committee to
          ----------------------
     reflect the extent to which the Company attains its goals with respect to
     the Financial Measures.

          Plan Year:  The period from January 1 until December 31.
          ---------

          Retirement:  A termination of employment initiated voluntarily by the
          ----------
     Participant (i) on or after age 65 or (ii) on or after age 55 with 10 years
     of participation service as credited under the Company's qualified defined
     benefit pension plan.

          Target Bonus Percentage:  A percentage of the Participant's salary
          -----------------------
     determined by the Committee at the beginning of the Plan Year.

          Waiver and Release:  The legal document in which the Participant (or
          ------------------
     the executor or administrator of the Participant's estate in the event of
     death), in exchange for amounts payable pursuant to Awards hereunder due to
     death, Disability or Retirement, releases the Company, its parents,
     subsidiaries and Related Entities (as defined in Section 8(d)(4)), their
     directors, officers, employees and agents, their employee benefit plans,
     and the fiduciaries and agents of said plans from liability and damages in
     any way related to the Participant's employment with or separation from the
     Company.  The Waiver and Release must be executed within 60 days after
     termination due to Disability or Retirement, or 180 days after termination
     due to death.

                                      -2-
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          2.   Administration.

          The Plan is administered by the Committee.  All decisions of the
Committee shall be binding and conclusive on the Participants.  Subject to the
provisions of the Plan, the Committee shall have the authority to:

          (a)  Select the Participants;

          (b)  Determine the Financial Measures and Performance Percentage for
each Plan Year, and the Target Bonus Percentage and Award Percentage for each
Participant;

          (c)  Determine the amounts payable pursuant to Awards; and

          (d)  Establish from time to time policies and procedures for the
administration of the Plan, interpret the Plan, and make all determinations
necessary or advisable for the administration of the Plan.

          3.   Participation.  Participants are selected by the Committee.  No
Employee shall at any time have the right (a) to be selected as a Participant,
(b) if so selected, to be entitled to an Award except under the specific terms
set forth in the Plan, or (c) if selected as a Participant in this Plan Year, to
be selected as a Participant in any subsequent plan year. Participants will be
notified in writing of their selection as Participants.

          4.   Target Bonus Percentage.

          (a)  The Committee will assign each Participant a Target Bonus
Percentage for the Plan Year, based on the position level of each Participant
and other considerations as the Committee deems appropriate.  The Target Bonus
Percentage will be assigned within 90 days after the beginning of the Plan Year,
unless the Participant was not an Employee on the first day of the Plan Year.

          (b)  An Employee who becomes a Participant after the first day of the
Plan Year will be assigned a Target Bonus Percentage, and will be eligible for
an Award in the manner calculated pursuant to Section 8, but unless otherwise
determined by the Committee, such Award shall be prorated to reflect the number
of days in the Plan Year in which such individual was a Participant.

          5.   Financial Measures.  Within 90 days after the beginning of the
Plan Year, the Committee will establish one or more objective performance goals
for the Plan Year with respect to the Financial Measures.  The performance goals
for each Plan Year shall be communicated to each Participant.

          6.   Performance Percentage. Within 90 days after the beginning of the
Plan Year, the Committee will establish an objective methodology for determining
the Performance

                                      -3-
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Percentage that will correspond with attained levels of performance under the
Financial Measures. Within 90 days following the end of the Plan Year, the
Committee will certify the Performance Percentage reached for the Plan Year.

          7.   Calculation of Awards.

          (a)  Each Participant's Award Percentage for the Plan Year will be
determined by multiplying the Participant's Target Bonus Percentage by the
Performance Percentage.

          (b)  Each Participant's Award payable for the Plan Year will be
determined by multiplying the Participant's Award Percentage by his or her Base
Salary.

          8.   Payment of Awards.

          The Committee has sole and absolute authority and discretion to
determine the time and manner in which Awards, if any, shall be paid under this
Plan.  The determination of the Committee, which shall be binding and conclusive
on any Participant, shall be communicated in writing to each Participant.
Generally, however, the following provisions apply:

          (a)  Form of Payment: Awards under the Plan are paid in the form of an
               ---------------
annual cash payment (the "Annual Award") and a long-term payout (the "Long-Term
Award").  The Long-Term Award shall become outstanding upon payment of the
Annual Award and shall vest over three years at one-third each year, subject to
the adjustment in Subsection (c) below, commencing on March 31 of the following
year (or such earlier date as shall be determined by the Committee). Payments
will be paid in cash subject to adjustments for such federal, state or local
taxes and other deductions, if any, as may be in effect at the time of payment.

          (b)  Timing of Payment of Annual Awards: Annual Awards will be paid
               ----------------------------------
within 90 days after the close of the Plan Year.  Notwithstanding the foregoing,
a Participant may elect to defer amounts payable pursuant to an Award under the
terms of any deferred compensation plan in which he or she is eligible to
participate.

          (c)  Timing of Payment of Long-Term Awards: Long-Term Awards will be
               -------------------------------------
paid in three annual installments, beginning approximately one year after the
payment of the Annual Award.  Amounts payable under the Long-Term Awards may be
adjusted downward by up to 20% annually and may be adjusted upward by any
amount, in the discretion of the Committee, based on the results of EBITDA, EVA
or other Financial Measures determined by the Committee during the payment
period.  The Committee retains full discretion to determine whether any
adjustments will be made based on Financial Measures, and this discretion is in
addition to the general discretion retained by the Committee in Subsection (d).

          (d)  Termination, Death or Disability:  Except as indicated below and
               --------------------------------
in Section 9, Annual Awards will be paid only to Participants who are actually
employed by and are on the payroll of the Company on the last day of the Plan
Year, and Long-Term Awards will be paid

                                      -4-
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only to Participants who are actually employed by and are on the payroll of the
Company on the date payments are made.

               (1)  A Participant whose employment terminates for any reason
          other than the circumstances described in Subsection (e)(2) or (3)
          prior to the last day of the Plan Year, shall forfeit any and all
          Awards.

               (2)  Those Participants whose employment terminates due to death,
          Disability or Retirement prior to the end of the Plan Year will, upon
          timely execution of a Waiver and Release, be paid a pro-rata portion
          of their Annual Award based on the number of days in the Plan Year
          prior to their date of termination. Such prorated payments will be
          made at the time and in the form that all payments are normally made
          to all other Participants. Those Participants whose employment
          terminates due to death, Disability or Retirement after the end of the
          Plan Year but prior to the date of payment of such Annual Award will,
          upon timely execution of a Waiver and Release, receive the full amount
          of such Annual Award to which they would otherwise be entitled. Such
          payments shall be made at the time and in the form that all Annual
          Award payments are normally made to all other Participants.

               (3)  Those Participants whose employment terminates due to death,
          Disability or Retirement will, upon timely execution of a Waiver and
          Release, be paid the remaining installments of any outstanding Long-
          Term Awards.  Such payments will be made as soon as practicable after
          the date of termination and shall be made without the adjustment of
          Subsection (c) above.

               (4)  If at any time during the Plan Year, a Participant commences
          employment with Lyondell Chemical Company or its subsidiaries, or
          LYONDELL-CITGO Refining, LP (a "Related Entity"), the Participant's
          Award shall be pro-rated based upon the number of days in the Plan
          Year prior to commencement of employment with the Related Entity.
          Such payments shall be made at the time and in the form that all
          payments are normally made to all other Participants.

               (5)  If a Participant's employment terminates because of death,
          the Participant's beneficiary or beneficiaries, designated by the
          Participant for purposes of this Plan in the manner prescribed by the
          Committee, or if there is no such designation, under the Company's
          Group Life Insurance Plan, or in the absence of any such beneficiary,
          the Participant's surviving spouse, or if there is no surviving
          spouse, the personal representative of such Participant's estate will,
          upon timely execution of a Waiver and Release by the executor or
          administrator of the Participant's estate, be entitled to receive the
          Award to which the Participant was entitled under this Section 8(d).

               (6)  Notwithstanding any provision in this Section 8 or any other
          provision of the Plan to the contrary, for purposes of determining
          whether a

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          Participant has terminated employment hereunder, the employment of a
          Participant shall not be deemed to have been terminated because of his
          absence from active employment on account of temporary illness or
          during authorized vacation or during temporary leaves of absence,
          granted by the Company for reasons of professional advancement,
          education, health or government service, or during military leave for
          any period if the Participant returns to active employment within 90
          days after the termination of his military leave, or during any period
          required to be treated as a leave of absence by virtue of any valid
          law or agreement.

               (7)  Notwithstanding any other provision of the Plan, the
          Committee, in its sole discretion, may permit continued participation,
          pro-ration or early distribution with respect to Awards that would
          otherwise be forfeited pursuant to the terms of the Plan.

          9.   Assignments and Transfers.  A Participant shall not assign,
encumber or transfer his rights and interests under the Plan, other than
pursuant to a marital settlement agreement or similar domestic relations
agreement, decree or order, and any attempt to do so shall render those rights
and interests null and void.

          10.  Finality of Determinations.  Any determination by the Company or
the Committee in carrying out or administering this Plan shall be final and
binding for all purposes and upon all interested persons and their heirs,
successors, and personal representatives.

          11.  Employee Rights under the Plan.  Neither the Plan nor any action
taken thereunder shall be construed as giving an Employee any right to be
retained in the employ of the Company. No Participant shall have any lien on any
assets of the Company by reason of any Award under this Plan.

          12.  Amendment, Suspension or Termination.  The Committee may amend,
suspend or terminate the Plan in whole or in part at any time.

                                                          EQUISTAR CHEMICALS, LP

                                      -6-<PAGE>

                                                                  EXHIBIT 4.1(b)

                           LYONDELL CHEMICAL COMPANY,

                             EQUISTAR CHEMICALS, LP

                                      AND

                     U.S. BANK TRUST, NATIONAL ASSOCIATION,

                                    TRUSTEE

                          THIRD SUPPLEMENTAL INDENTURE

                                  DATED AS OF

                                NOVEMBER 3, 2000

                                       TO

                                   INDENTURE

                                  DATED AS OF

                                 MARCH 10, 1992

              (AS SUPPLEMENTED BY THE FIRST SUPPLEMENTAL INDENTURE
             DATED AS OF MARCH 10, 1992 AND THE SECOND SUPPLEMENTAL
                    INDENTURE DATED AS OF DECEMBER 1, 1997)
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          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 U.S. Bank Trust, National Association (successor to
Continental Bank, National Association), as Trustee (the "Trustee"), supplements
the Indenture dated as of March 10, 1992, between Lyondell and the Trustee under
the Indenture, as supplemented by the First Supplemental Indenture dated as of
March 10, 1992 (the "First Supplemental Indenture"), pursuant to which the
9.125% Notes Due 2002 (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.

                                  SECTION TWO

                                   AMENDMENTS

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

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          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 last 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 last 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".

     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 last reference to "the Company" is changed to "such obligor".

                                       4
<PAGE>

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

     2.14  The first paragraph of Section 9.03 of the Indenture shall be amended
           so that (a) the first and third references to "The Company" are
           changed to "The Company, the Guarantor", (b) the second reference to
           "the Company" is changed to "the Company, the Guarantor", and (c) the
           fifth reference to "the Company" is changed to "the Company nor the
           Guarantor".

     2.15  The last paragraph of Section 9.03 of the Indenture shall be amended
           so that the reference to "The Trustee and the Company" is changed to
           "The Trustee, the Company and 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
<PAGE>

     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 in compliance
          with the provisions of the Indenture, 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 in compliance with the provisions of the
          Indenture, 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 U.S. Bank Trust, National Association 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

                              U.S. BANK TRUST, NATIONAL
                              ASSOCIATION, Trustee

                              By      /s/ JOHN D. BOWMAN
                                ----------------------------------------
                                     John D. Bowman
                                     Vice President

                                      11

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