<PAGE>
 
                                                                   EXHIBIT 10.35

                                                 EXHIBIT C TO FIRST AMENDMENT TO
                                                    MASTER TRANSACTION AGREEMENT




                               PARENT AGREEMENT



                                     AMONG



                        LYONDELL PETROCHEMICAL COMPANY,



                           MILLENNIUM CHEMICALS INC.



                          AND EQUISTAR CHEMICALS, LP
<PAGE>
 
                               TABLE OF CONTENTS
                               -----------------

                                                                       PAGE
                                                                       ----

SECTION 1  GUARANTEE OF OBLIGATIONS...................................   2
    1.1    Guarantee..................................................   2
    1.2    Guarantee Regarding Interested Owner Agreements............   2
    1.3    No Demand or Notice........................................   3
    1.4    Waiver of Resort to Security...............................   3
    1.5    No Discharge...............................................   3
    1.6    Waivers by the Parent......................................   3
    1.7    No Reduction...............................................   4
    1.8    Enforcement................................................   4
    1.9    Continued Effectiveness....................................   4
   1.10    Certain Defenses...........................................   4
   1.11    Parties in Interest........................................   4
  
SECTION 2  OWNERSHIP AND BUSINESS OF PARTNER SUBS.....................   5
    2.1    Restrictions on Transfer and Pledge of Partner Sub Stock...   5
    2.2    Right of First Option......................................   6
    2.3    Prohibition on Affiliated Obligor Bankruptcy, Etc..........   8
    2.4    Special Purpose Subsidiaries...............................   8
 
 SECTION 3 STANDSTILL AGREEMENT.......................................   8
 
     3.1   Standstill.................................................   8
     3.2   Exceptions.................................................   9
  
SECTION 4  MISCELLANEOUS..............................................   9
 
    4.1    No Waivers.................................................   9
    4.2    Expenses in Connection with Exercise.......................  10
    4.3    Subordination..............................................  10
    4.4    Confidentiality and Use of Information.....................  10
    4.5    Competing Businesses.......................................  10
    4.6    Further Assurances.........................................  10
    4.7    Successors and Assigns.....................................  10
    4.8    Benefits of Agreement Restricted to the Parties............  11
    4.9    Notices                                                      11
   4.10    Severability...............................................  12
   4.11    Termination................................................  12
   4.12    Construction and Certain Definitions.......................  12
   4.13    Counterparts...............................................  12
   4.14    Governing Law..............................................  12
   4.15    Jurisdiction; Consent to Service of Process; Waiver........  12
   4.16    Waiver of Jury Trial.......................................  13
   4.17    Dispute Resolution.........................................  13
   4.18    Amendment..................................................  13

                                      -i-
<PAGE>
 
APPENDICES

Appendix A     List of Related Agreements
Appendix B     Dispute Resolution Procedures




                                     -ii-
<PAGE>
 
                               PARENT AGREEMENT
                               ----------------

     This Parent Agreement (this "Agreement") is made as of this ____ day of
__________, 1997 among Lyondell Petrochemical Company, a Delaware corporation
("Lyondell"), Millennium Chemicals Inc., a Delaware corporation ("Millennium"
and, together with Lyondell, the "Parents")  and Equistar Chemicals, LP, a
Delaware limited partnership (the "Partnership").

     WHEREAS, Lyondell and Millennium entered into the Master Transaction
Agreement dated as of July 25, 1997, as amended (the "Master Transaction
Agreement").

     WHEREAS, Lyondell Petrochemical G.P. Inc. ("Lyondell GP") and Lyondell
Petrochemical L.P. Inc. ("Lyondell LP" and, together with Lyondell GP, the
"Lyondell Partner Subs") are both Delaware corporations and direct or indirect
wholly owned subsidiaries of Lyondell.

     WHEREAS, Millennium Petrochemicals GP LLC ("Millennium GP") and Millennium
Petrochemicals LP LLC ("Millennium LP" and, together with Millennium GP, the
"Millennium Partner Subs") are both Delaware limited liability companies and
direct or indirect wholly owned subsidiaries of Millennium.

     WHEREAS, pursuant to the terms of the Master Transaction Agreement, the
Partnership  has been formed under the laws of the State of Delaware pursuant to
the Limited Partnership Agreement being entered into simultaneously herewith (as
it may in the future be amended, supplemented, restated or otherwise modified or
amended, the "Partnership Agreement"), with Lyondell GP and Millennium GP as the
general partners and Lyondell LP and ML Partner as the limited partners of the
Partnership.  The Lyondell Partner Subs, together with any other direct or
indirect subsidiary of Lyondell that is a party to any of the Related Agreements
(as defined herein), are referred to herein as the "Lyondell Affiliated
Obligors."  The Millennium Partner Subs, together with any other direct or
indirect subsidiary of Millennium that is a party to any of the Related
Agreements, are referred to herein as the "Millennium Affiliated Obligors."  The
Lyondell Affiliated Obligors and the Millennium Affiliated Obligors,
collectively or individually as the context may require, are referred to herein
as the "Affiliated Obligors."  The Lyondell Partner Subs and the Millennium
Partner Subs, collectively or individually as the context may require, are
referred to herein as the "Partner Subs."

     WHEREAS, in connection with the closing of the transactions to be effected
pursuant to the Master Transaction Agreement, the Parents and certain of their
respective affiliates, have entered into or are entering into various agreements
and other legal documents, including the Partnership Agreement, services
agreements and asset contribution agreements (including this Agreement, the
"Related Agreements"), each of which is integrally related to the capitalization
and future operations of the Partnership and is listed on Appendix A hereto.
The Related Agreements (other than this Agreement) and any additional agreements
that may from time to time be added to Appendix A hereto by agreement of the
Parents, as they may in the future be amended, supplemented, restated or
otherwise modified, are referred to herein as the "Other Agreements".
<PAGE>
 
     WHEREAS, this Agreement is essential to the consummation of the closing
pursuant to the Master Transaction Agreement and the entering into and
effectiveness of the Other Agreements, and each of the parties to such
agreements is relying on this Agreement in connection with entering into each of
the Other Agreements.

     WHEREAS, in order to induce the parties thereto to enter into the Other
Agreements, each  Parent is willing, solely for the benefit of the Beneficiaries
(as defined below in Section 1.11) and their successors and assigns, to
guarantee the performance by its Affiliated Obligors of the obligations of such
Affiliated Obligors as set forth in this Agreement.

     WHEREAS, each Parent is willing to subject the Partner Sub Stock (as
defined herein) to certain restrictions on transfer, as set forth in this
Agreement.

     NOW THEREFORE, in, consideration of the foregoing and the mutual promises
and covenants of the parties hereto, the Parents and the Partnership hereby
agree as follows:


                                   SECTION 1
                           GUARANTEE OF OBLIGATIONS
                           ------------------------
 
     1.1  Guarantee.  Each Parent hereby unconditionally, absolutely and
irrevocably guarantees, undertakes and promises to cause, as herein provided,
the due and punctual payment and the full and prompt performance by its
Affiliated Obligors of all of the amounts to be paid and all of the terms and
provisions to be performed or observed by or on the part of its Affiliated
Obligors under the Other Agreements in accordance with the terms thereof (all
such terms and provisions as now or hereafter in existence being collectively
called the "Obligations") as follows: in the event that its Affiliated Obligors
shall fail in any manner whatsoever to pay, perform or observe any of their
Obligations, when and as the same shall be required to be paid, performed or
observed under the terms of the Other Agreements, such Parent will itself duly
and punctually pay, or fully and promptly perform or observe, as the case may
be, such Obligations, or cause the same to be duly and punctually paid, or fully
and promptly performed or observed, in each case as if such Parent were itself
the obligor with respect to such Obligations under the Other Agreements. Insofar
as this Section 1.1 relates to the obligations of an Affiliated Obligor under
the Partnership Agreement and except as set forth in Section 1.2, no Parent
shall be required to make, or cause a Partner Sub to make, any contribution to
the Partnership that such Partner Sub is not otherwise required to make pursuant
to the terms of Section 2.3, 2.4, or 12.2(d)(ii) of the Partnership Agreement.
Insofar as this Section 1.1 applies to Other Agreements other than the
Partnership Agreement, the term "Affiliated Obligors" will not include the
Partnership nor any partner in the Partnership in its capacity as such.

     1.2  Guarantee Regarding Interested Owner Agreements.  Each Parent
acknowledges that the Partnership Agreement sets forth definitions of
"Conflicted Partner" and "Nonconflicted Partner," and provides that a
Nonconflicted Partner has certain exclusive rights to control the Partnership
with respect to any Conflict Circumstance (as defined in the Partnership
Agreement); and accordingly, without limiting the rights of its Partner Sub
under Section 6.8 of the Partnership Agreement, each Parent hereby agrees to
cause its Partner Sub (i) to cause the Partnership to pay, 

                                      -2-
<PAGE>
 
perform and observe all of the Obligations to be paid, performed or observed by
or on the part of the Partnership under the Other Agreements, in accordance with
the terms thereof, to the extent that such Partner Sub is the Nonconflicted
Partner and is thereby entitled to cause the payment, performance and observance
of such Obligations and (ii) to abide by its obligations as the Nonconflicted
Partner with respect to any Conflict Circumstance in accordance with the terms
of the Partnership Agreement applicable thereto; provided, however, that each
Parent's responsibility under this Section 1.2 for a failure of the Partnership
to pay, perform or observe its obligations under the Other Agreements shall be
limited to the circumstances in which the Partnership's failure to so pay,
perform or observe its obligations under the Other Agreements was directly
caused by an act or failure to act of its Partner Sub; provided, further, that
nothing in this Section 1.2 shall require a Parent to make or cause such Partner
Sub to make any contribution to the Partnership that such Partner Sub is not
otherwise required to make pursuant to Section 2.3, 2.4, or 12.2(d)(ii) of the
Partnership Agreement.

     1.3  No Demand or Notice.  It shall not be a condition to the guarantees
and agreements set forth in Sections 1.1 and 1.2 above (together, the
"Guarantee") that a Beneficiary shall have first made any request of or demand
upon, or given any notice of the occurrence of a default under the Other
Agreements or any other notice whatsoever to, either Parent or its Affiliated
Obligors or any other Person, or shall have instituted any action or proceeding
against any Affiliated Obligor or any other Person in respect thereof, or shall
have joined any Affiliated Obligor or the Partnership in any such action or
proceeding. A Beneficiary in asserting the benefit of the Guarantee shall give
prompt notice to a Parent of any failure by its Affiliated Obligors or the
Partnership to pay, perform or observe any Obligation; provided, however, that
any failure, delay or defect in the giving of such notice shall not alter or
affect the Guarantee under this Agreement.

     1.4  Waiver of Resort to Security.  Each Parent further agrees that this
Agreement, insofar as it constitutes a guarantee of monetary Obligations,
constitutes a guarantee of payment when due and not of collection, and each
Parent waives any right to require as a condition to its Guarantee that any
resort be had by a Beneficiary to any security held for the payment of any
Obligations.

     1.5  No Discharge.  The Guarantee is and shall remain absolute and
unconditional irrespective of any circumstance that might otherwise constitute a
legal or equitable discharge of a surety or guarantor, as the case may be, with
respect to its Guarantee.

     1.6  Waivers by the Parent.  Each Parent hereby waives, with respect to the
Guarantee but without prejudice to the rights of the parties to the several
Other Agreements, any notice of acceptance of this Agreement, grace,
presentment, demand, protest, notice of the occurrence of a default under the
Other Agreements and any other notice of any kind whatsoever and promptness in
making any claim or demand hereunder. The Guarantee shall not be affected by (i)
the failure of a Beneficiary to assert any claim or demand or to enforce any
right or remedy under the provisions of any of the Other Agreements or any
agreement related thereto or otherwise, (ii) any extension or renewal of any of
the Other Agreements or any agreement related thereto, (iii) any rescission,
waiver, amendment or modification of any of the terms or provisions of any of
the Other Agreements or of any agreement related thereto, including, without
limitation, any change in the time, manner 

                                      -3-
<PAGE>
 
or place of payment or performance of any of the obligations under the Other
Agreements, or (iv) the release of any security held for payment of any
Obligations.

     1.7  No Reduction.  The Guarantee shall not be subject to any reduction,
limitation, impairment or termination for any reason, including, without
limitation, any claim of waiver, release, surrender, alteration or compromise,
and shall not be subject to any defense or set-off, counterclaim, recoupment or
termination whatsoever, except as provided in Section 1.10.

     1.8  Enforcement.  Notwithstanding anything herein to the contrary, a
Beneficiary may proceed to enforce the Guarantee without first pursuing or
exhausting any right or remedy that it or any of its successors or assigns may
have against any Affiliated Obligor or either Parent or any other person.

     1.9  Continued Effectiveness.  The Guarantee shall continue to be effective
or be reinstated, as the case may be, if at any time payment, or any part
thereof, of any Obligation of an Affiliated Obligor is rescinded or must
otherwise be restored or returned by the Person receiving such payment upon the
insolvency, bankruptcy or reorganization of an Affiliated Obligor, all as though
such payment or part thereof had not been made.

     1.10  Certain Defenses.  Nothing herein is intended to deny to either
Parent, and it is expressly agreed that each Parent shall have and may assert,
any and all of the defenses, set-offs, counterclaims and other rights (other
than those relating to insolvency, bankruptcy or reorganization as described in
Section 1.9) with regard to any Obligations that its Affiliated Obligors may
possess except any defense its Affiliated Obligors may possess relating to lack
of validity or enforceability of the Other Agreements or any other agreement or
instrument relating thereto as against its Affiliated Obligors arising from the
defective incorporation or other defective organization of its Affiliated
Obligors, their lack of qualification to do business in any applicable
jurisdiction or their defective corporate or other organizational authority to
enter into, deliver or perform the Other Agreements.

     1.11  Parties in Interest.  This Agreement shall inure solely to the
benefit of the Beneficiaries, each of whom has the right to enforce the
Guarantee against the Parents, and nothing in this Agreement, express or
implied, is intended to or shall confer upon any other Person any rights,
benefits or remedies of any nature whatsoever under or by reason of this
Agreement. As used in this Agreement, "Beneficiaries" shall mean (i) as to any
obligations of Millennium hereunder, the Partnership, Lyondell and the Lyondell
Affiliated Obligors, and (ii) as to any obligations of Lyondell hereunder, the
Partnership, Millennium and the Millennium Affiliated Obligors. As used in this
Agreement, the term Parent includes any successor or transferee of the Parent,
and the term Affiliated Obligors includes any successor to or transferee of the
Affiliated Obligors' interest in the Partnership permitted pursuant to the
Partnership Agreement.

                                      -4-
<PAGE>
 
                                   SECTION 2
                    OWNERSHIP AND BUSINESS OF PARTNER SUBS
                    --------------------------------------
 
     2.1  Restrictions on Transfer and Pledge of Partner Sub Stock.  (a) Each
Parent agrees that except as otherwise provided below in this Section 2.1 or
Section 2.2 or with the written consent of the other Parent (or any Successor
Parent, as defined in Section 2.1(d)), which consent may be granted or withheld
in such Parent's sole discretion, it will not, in any transaction or series of
transactions, directly or indirectly, (i) sell, assign or otherwise in any
manner dispose of, whether by act, deed, merger or otherwise ("Transfer") or
(ii) mortgage, pledge, encumber or create or suffer to exist any pledge, lien or
encumbrance upon or security interest in ("Pledge"), all or any part of the
capital stock (including any securities convertible into or exchangeable for or
carrying any rights to purchase, subscribe for or otherwise acquire any such
capital stock) of its Partner Subs (collectively, the "Partner Sub Stock").
(Each of the defined terms "Transfer"and "Pledge" is used herein both as a noun
and as a verb.) Any attempt by a Parent to Transfer or Pledge all or a portion
of its Partner Sub Stock in violation of this Agreement shall be void ab initio
and shall not be effective to transfer such Partner Sub Stock or any portion
thereof. The Partnership Agreement contains provisions relating to the Transfer
and Pledge of the Partner Subs' direct interests in the Partnership.

     (b)  The Parent agrees that all certificates representing shares of Partner
Sub Stock, whether currently owned or hereafter acquired, shall carry the
following legend, which legend each Parent agrees to cause to be placed thereon
and to cause to remain thereon as long as such shares are subject to the
restrictions of this Agreement:

     THE SALE, ASSIGNMENT, PLEDGE OR OTHER TRANSFER OR HYPOTHECATION OF THE
     STOCK REPRESENTED BY THIS CERTIFICATE IS SUBJECT TO CERTAIN RESTRICTIONS
     PURSUANT TO AND MAY NOT BE EFFECTED EXCEPT IN ACCORDANCE WITH THE
     PROVISIONS OF AN AGREEMENT BINDING UPON THE OWNER OF THE STOCK REPRESENTED
     HEREBY.  THE OWNER OR ISSUER WILL FURNISH A COPY OF SUCH AGREEMENT TO ANY
     PROPOSED TRANSFEREE OR PLEDGEE WITHOUT CHARGE UPON REQUEST.

     (c)  Without the need for the consent of any Person, any Parent may
Transfer its Partner Sub Stock to any wholly-owned Affiliate of such Parent.

     (d)  Each Parent may Transfer all (but not less than all) of its Partner
Sub Stock if such Transfer is in connection with (i) a merger, consolidation,
conversion or share exchange of such Parent or (ii) a sale or other disposition
of (x) the Partner Sub Stock plus (y) other assets representing at least fifty
percent (50%) of the book value of such Parent's assets excluding the Partner
Sub Stock, as reflected on its most recent audited consolidated (or combined)
financial statements; provided, however, the ultimate parent entity of the
acquiring, succeeding or surviving entity in any such transaction (the
"Successor Parent") (i) shall succeed to and be substituted for such Parent,
with the same effect as if it had been named herein and (ii) shall execute an
instrument wherein such ultimate parent entity shall agree to be bound by the
obligations of such Parent under this Agreement, with the same effect as if it
had been named herein, whereupon, unless such Parent shall 


                                      -5-
<PAGE>
 
become a direct or indirect subsidiary of the Successor Parent, such Parent
shall thereupon be released from all obligations hereunder.

     (e)  Nothing in this Agreement shall prevent the Transfer or Pledge of the
capital stock, equity ownership interests or other securities of a Parent, and
no such Transfer or Pledge of securities issued by a Parent shall be deemed to
constitute a Transfer or Pledge of Partner Sub Stock hereunder.

     (f)  Each Parent may Pledge all (but not less than all) of its Partner Sub
Stock to any one or more Approved Lenders; provided that the Pledge shall be
evidenced by an instrument, reasonably satisfactory to the Partnership, wherein
the Approved Lender receiving such Pledge shall agree that in the event such
Approved Lender obtains a right of foreclosure on such Parent's Partner Sub
Stock, such Approved Lender will foreclose on the Partner Sub Stock of each of
such Parent's Partner Subs equally so that such Approved Lender will in all
events hold equal portions of Partner Sub Stock of LG Partner and Lyondell LP or
Millennium GP and Millennium LP, as the case may be.  An "Approved Lender" shall
be any bank, insurance company, investment bank or other financial institution
that is regularly engaged in the business of making loans.

     2.2  Right of First Option.

          (a)  Without the consent of the other Parent, neither Parent may
Transfer less than all of its Partner Sub Stock.  Unless such Transfer is
otherwise permitted by Section 2.1, any Parent desiring to Transfer (pursuant to
a cash sale) all of its Partner Sub Stock (the "Selling Parent") shall give
written notice (the "Initial Notice") to the Partnership and the other Parent
(the "Offeree Parent") stating that the Selling Parent desires to Transfer its
Partner Sub Stock and stating the cash purchase price and all other terms on
which it is willing to sell (the "Offer Terms").  Delivery of an Initial Notice
shall constitute the irrevocable offer of the Selling Parent to sell its Partner
Sub Stock to the Offeree Parent hereunder.

          (b)  The Offeree Parent shall have the option, exercisable by
delivering written notice (the "Acceptance Notice") of such exercise to the
Selling Parent within 45 days of the date of the Initial Notice, to elect to
purchase all of the Partner Sub Stock of the Selling Parent on the Offer Terms
described in the Initial Notice.  The Acceptance Notice shall set a date for
closing the purchase, such date to be not less than 30 nor more than 90 days
after delivery of the Acceptance Notice; provided that such time period shall be
subject to extension as reasonably necessary (up to a maximum of an additional
120 days after such 90 day period) in order to comply with any applicable filing
and waiting period requirements under the Hart-Scott-Rodino Antitrust
Improvements Act.  The closing shall be held at the Partnership's offices.  The
purchase price for the Selling Parent's Partner Sub Stock shall be paid in cash
delivered at the closing.  The purchase shall be consummated by appropriate and
customary documentation (including the giving of representations and warranties
substantially similar to those set forth in Sections 2.1 through 2.4 of the
Master Transaction Agreement and customary representations and warranties
regarding the Selling Parent's title to its Partner Sub Stock).

          (c)  If the Offeree Parent does not elect to purchase the Selling
Parent's Partner Sub Stock within 45 days after the receipt of the Initial
Notice, the Selling Parent shall have a further 


                                      -6-
<PAGE>
 
180 days during which it may, subject to Sections 2.2(d) and (e), consummate the
sale of its Partner Sub Stock to a third party purchaser at a purchase price and
on such other terms that are no more favorable to such purchaser than the Offer
Terms. If the sale is not completed within such further 180-day period, the
Initial Notice shall be deemed to have expired and a new notice and offer shall
be required before the Selling Parent may make any Transfer of its Partner Sub
Stock.

          (d)  Before the Selling Parent may consummate a Transfer of its
Partner Sub Stock to a third party in accordance with this Agreement, the
Selling Parent shall demonstrate to the Partnership that such proposed purchaser
(or the Person willing to serve as its guarantor as contemplated by Section
2.2(f)) has outstanding indebtedness that is rated investment grade by either
Moody's Investor Services Inc. or Standard & Poor's Corporation, or if such
proposed purchaser (or such other Person) has no rated indebtedness outstanding,
such Person shall provide an opinion from a nationally recognized investment
banking firm that it could be reasonably expected to obtain such a rating.

          (e)  Notwithstanding the foregoing provisions of this Section 2.2, a
Parent may Transfer its Partner Sub Stock (other than pursuant to Section 2.1)
only if all of the following occur:

               (i)   The Transfer is accomplished in a non-public offering in
          compliance with, and exempt from, the registration and qualification
          requirements of all federal and state securities laws and regulations.

               (ii)  The Transfer does not cause a default under any material
          contract to which the Partnership is a party or by which the
          Partnership or any of its properties is bound.

               (iii) The transferee executes an appropriate agreement to be
          bound by this Agreement.

               (iv)  The transferor and/or transferee bears all reasonable costs
          incurred by the Partnership in connection with the Transfer.

               (v)   The transferee (or the guarantor of the obligations of the
          transferee) satisfies the criteria set forth in Section 2.2(d) and
          delivers an agreement to the other Parent and the Partnership
          substantially in the form of this Agreement.

               (vi)  The proposed transferor is not in default in the timely
          performance of any of its material obligations to the Partnership.

               (vii) The provisions of Section 2.2(f) are satisfied.

          (f)  Neither Parent may Transfer the Partner Sub Stock of either of
its Partner Subs to any Person unless such Parent simultaneously Transfers the
Partner Sub Stock of its other Partner Sub to such Person or a wholly-owned
Affiliate (as defined in the Partnership Agreement) of such Person.


                                      -7-
<PAGE>
 
     2.3  Prohibition on Affiliated Obligor Bankruptcy, Etc. Each Parent hereby
agrees that it will not, without the written consent of the other Parent, permit
any of its Affiliated Obligors (or their successors or assigns) (i) to commence
a voluntary action under the Federal bankruptcy laws, as now or hereafter
constituted, or any other applicable Federal or State bankruptcy, insolvency or
other similar law, (ii) to institute a proceeding to be adjudicated a voluntary
bankrupt, (iii) to consent to the filing of a bankruptcy proceeding against it,
(iv) to fail to contest a bankruptcy proceeding against it, (v) to consent to
the appointment of a receiver, custodian, liquidator or trustee for it or for
all or any substantial portion of its property, (vi) in the case of its Partner
Subs, to issue or sell other than to such Parent any of its own Partner Sub
Stock or (vii) to effect, recognize or permit any transfer of any of its own
Partner Sub Stock other than in accordance with the provisions of Section 2 of
this Agreement.

     2.4  Special Purpose Subsidiaries.  Each Parent agrees that (i) the
business of its Partner Subs shall be restricted solely to the holding of the
respective interests in the Partnership and the doing of things necessary or
incidental in connection therewith, and (ii) it will cause its Partner Subs not
to own any assets, incur any liabilities or engage, participate or invest in any
business outside the scope of their businesses as described in clause (i); 
provided, however, that this Section 2.4 shall not apply with respect to any 
Wholly Owned Affiliates to whom such Partner Subs shall transfer their 
respective interests in the Partnership if such Wholly Owned Affiliates are not 
bound by Section 9.6 of the Partnership Agreement.


                                   SECTION 3
                             STANDSTILL AGREEMENT
                             --------------------
 
     3.1  Standstill.  Each Parent agrees that, until the expiration of 24
months from the date on which either such Parent and its Affiliates or the other
Parent and its Affiliates no longer hold an interest in the Partnership, neither
it, nor any of its Affiliated Obligors or other subsidiaries, shall, without
prior written approval of the other Parent: (i) in any manner acquire, agree to
acquire or make any proposal to acquire, directly or indirectly, any securities,
assets or property of the other Parent (other than such Parent's Partner Sub
Stock or the interests in the Partnership held by such Parent's Partner Subs),
whether such agreement or proposal is made with or to the other Parent or a
third party; (ii) make any unsolicited proposal to enter into, directly or
indirectly, any merger or other business combination involving the other Parent;
(iii) make, or in any way participate, directly or indirectly, in any
"solicitation" of "proxies" (as such terms are used in the proxy rules of the
Securities and Exchange Commission) to vote, or seek to advise or influence any
person with respect to the voting of, any voting securities of the other Parent;
(iv) form, join or in any way participate in a "group" (within the meaning of
Section 13(d)(3) of the Securities Exchange Act of 1934) with respect to any
voting securities of the other Parent; (v) otherwise act, alone or in concert
with others, to seek to control or influence the management, Board of Directors
or policies of the other Parent (other than with respect to the ownership,
business, property and affairs of the Partnership); (vi) disclose any intention,
plan or arrangement inconsistent with the foregoing; or (vii) advise, encourage,
provide assistance (including financial assistance) to or hold discussions with
any other persons in connection with any of the foregoing. Each Parent also
agrees during such period not to: (i) request the other Parent (or its
directors, officers, employees or agents), directly or indirectly, to amend or
waive any provision of this Section 3.1 (including this sentence); or (ii) take
any action which might reasonably be expected to require the other Parent to
make a public announcement regarding the possibility of a business combination
or merger.


                                      -8-
<PAGE>
 
     3.2  Exceptions.  Notwithstanding the provisions of Section 3.1:

     (a)  Either Parent may, by notice to the other, terminate the provisions of
Section 3.1 (as applied to both Parents) at any time within 30 days after the
occurrence of any of the following events with respect to the other Parent:  (i)
a Change of Control (as defined below) of such other Parent shall have occurred,
(ii) such other Parent shall have entered into a definitive agreement providing
for, or publicly announced its intention to effect, any transaction involving a
Change of Control of such other Parent or (iii) a tender offer or exchange offer
shall have been commenced or publicly announced that, if consummated, would have
the effect with respect to such other Parent described in clause (c) of the
definition of "Change of Control."  A "Change of Control" of a Parent shall mean
the occurrence of any of the following events:  (a) there shall be consummated
any consolidation, merger or share exchange of such Parent (i) in which such
Parent is not the continuing or surviving Person (other than a consolidation,
merger or share exchange with a wholly owned subsidiary of such Parent in which
all shares of common stock of such Parent outstanding immediately prior to the
effectiveness thereof are changed into or exchanged for the same number of
shares of common stock of such subsidiary) or (ii) pursuant to which the common
stock of such Parent is converted into cash, securities or other property, other
than, in each case, a consolidation, merger or share exchange of such Parent in
which the holders of the common stock immediately prior to the consolidation,
merger or share exchange hold, directly or indirectly, at least a majority of
the voting power and common equity of the continuing or surviving Person
immediately after such consolidation, merger or share exchange; (b) such
Parent's properties and assets are sold or otherwise disposed of substantially
as an entirety on a consolidated basis to any Person or group of Persons in any
one transaction or a series of related transactions, other than as contemplated
by the Master Transaction Agreement; or (c) any Person or any Persons acting
together which would constitute a "group" (as defined in Section 3.1) (other
than such Parent, any subsidiary of such Parent, any employee stock purchase
plan, stock option plan or other stock incentive plan or program, retirement
plan or automatic dividend reinvestment plan or any substantially similar plan
of such Parent or any subsidiary of such Parent or any Person holding securities
of such Parent for or pursuant to the terms of any such employee benefit plan),
together with any affiliates thereof, shall acquire beneficial ownership (as
defined in Rule 13d-3 under the Securities Exchange Act of 1934) of 50% or more
of the voting stock of such Parent.

     (b)  The terms of the first sentence of Section 3.1 shall not be applicable
to the purchase and sale of any securities of the other Parent by independent
third-party managers of any pension or other related employee benefit plans who
are acting as passive investors in the other Parent.


                                   SECTION 4
                                 MISCELLANEOUS
                                 -------------
 
     4.1  No Waivers.  No failure or delay by a Beneficiary or a Parent in
exercising any right or power under this Agreement, or any single or partial
exercise of any such right or power, shall preclude any other or further
exercise thereof or the exercise of any other right or power. Such single or
partial exercise of any right or power shall be cumulative and not exclusive of
any rights or remedies provided by law.

                                      -9-
<PAGE>
 
     4.2  Expenses in Connection with Exercise.  In the event of a dispute
between parties hereto regarding the exercise or enforcement of any of the
rights of a Beneficiary under this Agreement or the failure by a Parent to
perform or observe any of the provisions of this Agreement, the party that does
not ultimately prevail in such dispute shall be liable, and hereby agrees, to
reimburse, on demand, each other such party for any and all costs and expenses,
including the fees and expenses of legal counsel and of any other counsel,
experts, consultants or agents, that such other party may incur in connection
therewith.

     4.3  Subordination.  The rights of a Parent against its Affiliated Obligors
arising from any payment or performance by a Parent hereunder shall be
subordinate in all respects to the rights of the Beneficiaries against such
Affiliated Obligors, and such Parent shall not compete in any way with a
Beneficiary in any winding-up or dissolution of such Affiliated Obligors unless
and until all sums due and to become due from such Affiliated Obligors to the
Beneficiaries have been paid in full. If any amount shall be paid to a Parent in
violation of this Section, such amount shall be held in trust for the benefit of
the Beneficiaries and shall forthwith be paid to the Beneficiaries to be
credited and applied to any sums owed or to be owed by such Parent's Affiliated
Obligors. Subject to the foregoing, upon payment of all sums due or to become
due by Affiliated Obligors to the Beneficiaries, the Parent of such Affiliated
Obligors shall be subrogated to the rights of the Beneficiary against such
Affiliated Obligors, and the Beneficiaries agree to take at such Parent's
expense such steps as such Parent may reasonably request to implement such
subrogation.

     4.4  Confidentiality and Use of Information.  (a) Each Parent agrees to be
bound by the terms and conditions of Section 13.1 of the Partnership Agreement
as if such Parent was a "Partner" as defined in such agreement.

     (b)  The Parents shall consult with each other on an ongoing basis with
respect to disclosures regarding the Partnership and its business and affairs
that each is required to make in reports filed from time to time with the
Securities and Exchange Commission.

     4.5  Competing Businesses.  If either Parent desires to initiate or pursue
any opportunity to undertake, engage in, acquire or invest in a Business
Opportunity (as such term is defined in the Partnership Agreement), such Parent
agrees to offer such Business Opportunity to the Partnership under the terms and
conditions set forth in Sections 9.3(c) and (d) of the Partnership Agreement as
if such Parent were the "Proposing Partner" (as defined in the Partnership
Agreement) with respect thereto, and in such event the Partnership shall have
the rights and obligations with respect thereto set forth in such Sections
9.3(c) and (d).

     4.6  Further Assurances.  From time to time, each Parent agrees to execute
and deliver such additional documents and provide such additional information
and assistance as the Beneficiaries may reasonably require to carry out the
terms of this Agreement.

     4.7  Successors and Assigns.  Except as may be expressly provided herein,
this Agreement shall be binding upon and inure to the benefit of the successors
of the Beneficiaries. Except as provided in this Agreement and except that a
Parent may assign its rights or obligations under this Agreement to a third
party in connection with a transfer of direct interests in the Partnership owned


                                     -10-
<PAGE>
 
by its Partner Subs if such transfer is permitted and consummated in accordance
with the Partnership Agreement, no Parent may assign or delegate any of its
rights or obligations under this Agreement without the prior written consent of
all the Beneficiaries, which consent shall be in the sole and absolute
discretion of such Beneficiaries. Any purported assignment or delegation without
such consent shall be void and ineffective.

     4.8  Benefits of Agreement Restricted to the Parties.  This Agreement is
made solely for the benefit of the Beneficiaries (as defined in Section 1.11),
and no other Person shall have any right, claim or cause of action under or by
virtue of this Agreement.

     4.9  Notices.  All notices, requests, demands and other communications
(collectively, "notices") required or may be given under this Agreement shall be
in writing and shall be deemed to have been duly given if and when (i)
transmitted by telecopier facsimile with proof of confirmation from the
transmitting machine or (ii) delivered by commercial courier or other hand
delivery, as follows:

If to Lyondell                            If to the Lyondell Partner Subs

 
Lyondell Petrochemical Company            c/o Lyondell Petrochemical Company 
1221 McKinney Street                      1221 McKinney Street                
Houston, Texas 77010                      Houston, Texas 77010                
Attention:  Jeffrey R. Pendergraft        Attention:  Jeffrey R. Pendergraft  
Telecopy Number: (713) 652-4538           Telecopy Number: (713) 652-4538     
                                                                              

If to Millennium                          If to the Millennium Partner Subs


Millennium Chemicals Inc.                 c/o Millennium Chemicals Inc.       
99 Wood Avenue South                      99 Wood Avenue South                 
Iselin, New Jersey  08830                 Iselin, New Jersey  08830            
Attention:  George H. Hempstead, III      Attention:  George H. Hempstead, III 
Telecopy Number: (908) 603-6857           Telecopy Number: (908) 603-6857      

                                                                               
If to the Partnership

______________________________
______________________________
______________________________
Attention:____________________
Telecopy Number:______________

or to such other address as such Parent or Beneficiary shall have specified by
notice to the other Parent.

                                     -11-
<PAGE>
 
     4.10  Severability.  In the event that any provisions of this Agreement
shall finally be determined to be unlawful, such provision shall, so long as the
economic and legal substance of the transactions contemplated hereby is not
affected in any materially adverse manner as to any party hereto, be deemed
severed from this Agreement and every other provision of this Agreement shall
remain in full force and effect.

     4.11  Termination.  Except for Sections 3.1 and 3.2, this Agreement shall
terminate and be of no further force and effect as to a Parent (i) as and when
provided in Section 2.1(d) or (ii) if and when such Parent Transfers all of its
Partner Sub Stock in a transaction permitted by Section 2.2; provided, however,
that such termination shall not discharge (x) any accrued Obligations owed by a
Parent as of the date of such termination or (y) any Obligations, whether
arising before or after such termination, under such Parent's Asset Contribution
Agreement or any Related Agreement executed pursuant to such Asset Contribution
Agreement. In addition, the Guarantee by a Parent of Obligations of an
Affiliated Obligor other than a Partner Sub shall terminate as and when the
Parent ceases to own any stock of such Affiliated Obligor, insofar as such
Guarantee relates to Obligations arising thereafter.

     4.12  Construction and Certain Definitions.

     (a)   In construing this Agreement, the following principles shall be
followed:  (i) no consideration shall be given to the captions of the articles,
sections, subsections or clauses, which are inserted for convenience in locating
the provisions of this Agreement and not as an aid in construction; (ii) no
consideration shall be given to the fact or presumption that any party hereto
had a greater or lesser hand in drafting this Agreement; (iii) examples shall
not be construed to limit, expressly or by implication, the matter they
illustrate; (iv) the word "includes" and its syntactic variants mean "includes,
but is not limited to" and corresponding syntactic variant expressions; (v) the
plural shall be deemed to include the singular, and vice versa; (vi) each gender
shall be deemed to include the other gender; and (vii) each exhibit, attachment
and schedule to this Agreement is a part of this Agreement.

     (b)   The term "Person" shall mean any natural person or any corporation,
partnership, limited liability company, joint venture, association, trust or
other entity or organization.

     4.13  Counterparts.  This Agreement may be executed in one or more
counterparts, each of which shall constitute an original, and all of which when
taken together shall constitute one and the same original document.

     4.14  Governing Law.  The laws of the State of Delaware shall govern the
construction, interpretation and effect of this Agreement without giving effect
to any conflicts of law principles.

     4.15  Jurisdiction; Consent to Service of Process; Waiver.  ANY JUDICIAL
PROCEEDING BROUGHT AGAINST ANY PARTY TO THIS AGREEMENT OR ANY DISPUTE UNDER OR
ARISING OUT OF OR IN CONNECTION WITH THIS AGREEMENT OR ANY MATTER RELATED HERETO
SHALL BE BROUGHT IN THE FEDERAL OR STATE COURTS OF THE STATE OF DELAWARE, AND,
BY EXECUTION AND DELIVERY OF 

                                     -12-
<PAGE>
 
THIS AGREEMENT, EACH OF THE PARTIES TO THIS AGREEMENT ACCEPTS THE EXCLUSIVE
JURISDICTION OF SUCH COURTS AND IRREVOCABLY AGREES TO BE BOUND BY ANY JUDGMENT
(AS FINALLY ADJUDICATED) RENDERED THEREBY IN CONNECTION WITH THIS AGREEMENT.
EACH OF THE PARTIES TO THIS AGREEMENT SHALL APPOINT THE CORPORATION TRUST
COMPANY, THE PRENTICE-HALL CORPORATION SYSTEM, INC. OR A SIMILAR ENTITY (THE
"AGENT") AS AGENT TO RECEIVE ON ITS BEHALF SERVICE OF PROCESS IN ANY PROCEEDING
IN ANY SUCH COURT IN THE STATE OF DELAWARE. THE FOREGOING CONSENTS TO
JURISDICTION AND APPOINTMENTS OF AGENT TO RECEIVE SERVICE OF PROCESS SHALL NOT
CONSTITUTE GENERAL CONSENTS TO SERVICE OF PROCESS IN THE STATE OF DELAWARE FOR
ANY PURPOSE EXCEPT AS PROVIDED ABOVE AND SHALL NOT BE DEEMED TO CONFER RIGHTS ON
ANY PERSON OTHER THAN THE PARTIES HERETO. EACH PARENT HEREBY WAIVES ANY
OBJECTION IT MAY HAVE BASED UPON LACK OF PERSONAL JURISDICTION, IMPROPER VENUE
OR FORUM NON-CONVENIENS.

     4.16  Waiver of Jury Trial.  EACH PARTY HEREBY KNOWINGLY AND INTENTIONALLY,
IRREVOCABLY AND UNCONDITIONALLY WAIVES TRIAL BY JURY IN ANY LEGAL ACTION OR
PROCEEDING RELATING TO THIS AGREEMENT AND FOR ANY COUNTERCLAIM THEREIN.

     4.17  Dispute Resolution.  All disputes under this Agreement shall be
resolved in accordance with the Dispute Resolution Procedures set forth in
Appendix B.

     4.18  Amendment.  All waivers, modifications, amendments or alterations of
this Agreement shall require the execution of a written instrument signed by
each of the parties hereto.



                           [signature page follows]

                                     -13-
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have executed and delivered this
Guarantee Agreement as of the date first above written.



                              LYONDELL PETROCHEMICAL COMPANY



                              By:______________________________
                                    Name:
                                    Title:

                              MILLENNIUM CHEMICALS INC.



                              By:______________________________
                                    Name:
                                    Title:

                              EQUISTAR CHEMICALS, LP



                              By:______________________________
                                    Name:
                                    Title:



                                     -14-
<PAGE>
 
                                  APPENDIX A
                                      TO
                               PARENT AGREEMENT


                          LIST OF RELATED AGREEMENTS
                          --------------------------


          1.   Partnership Agreement

          2.   Lyondell Note

          3.   Asset Contribution Agreements

               a.   From Lyondell to the Partnership

               b.   From Millennium to the Partnership

          4.   [List here all agreements listed as Tier 2 Agreements in Master
               Transaction Agreement]



                                      A-1
<PAGE>
 
                                  APPENDIX B
                                      TO
                               PARENT AGREEMENT


                         DISPUTE RESOLUTION PROCEDURES
                         -----------------------------


     (1)  Binding and Exclusive Means.  The dispute resolution provisions set
forth in this Appendix B shall be the binding and exclusive means to resolve all
disputes arising under this Agreement (each a "Dispute").

     (2)  Standards and Criteria.  In resolving any Dispute, the standards and
criteria for resolving such dispute shall, unless the Parents in their
discretion jointly stipulate otherwise, be as set forth in Appendix 1 to this
Appendix B.

     (3)  ADR and Binding Arbitration Procedures.  If a Dispute arises, the
following procedures shall be implemented:

     (a)  The Parent from whom recovery is sought may at any time invoke the
dispute resolution procedures set forth in this Appendix B as to any Dispute by
providing written notice of such action to the other Parent, who within five
Business Days after such notice shall schedule a meeting to be held in Houston,
Texas between the Parents.  The meeting shall occur within 10 Business Days
after notice of the meeting is delivered to the other Parent.  The meeting shall
be attended by representatives of each Parent having decision-making authority
regarding the Dispute as well as the dispute resolution process and who shall
attempt in a commercially reasonable manner to negotiate a resolution of the
Dispute.

     (b)  The representatives of the Parents shall cooperate in a commercially
reasonable manner and shall explore whether techniques such as mediation,
minitrials, mock trials or other techniques of alternative dispute resolution
might be useful.  In the event that a technique of alternative dispute
resolution is so agreed upon, a specific timetable and completion date for its
implementation shall also be agreed upon.  The representatives will continue to
meet and discuss settlement until the date (the "Interim Decision Date") that is
the earliest to occur of the following events: (i) an agreement shall be reached
by the Parents resolving the Dispute; (ii) one of the Parents shall determine
and notify the other Parent in writing that no agreement resolving the Dispute
is likely to be reached; (iii) if a technique of alternative dispute resolution
is agreed upon, the completion date therefor shall occur without the Parents
having resolved the Dispute; or (iv) if another technique of alternative dispute
resolution is not agreed upon, two full meeting days (or such other time period
as may be agreed upon) shall expire without the Parents having resolved the
Dispute.

     (c)  If, as of the Interim Decision Date, the Parents have not succeeded in
negotiating a resolution of the dispute pursuant to subsection (b), the Parents
shall proceed under subsection (d).


                                      B-1
<PAGE>
 
     (d)  The Parents agree to appoint a mutually acceptable neutral person not
affiliated with any of the Parents (the "Neutral").  If the Parents have been
unable to agree upon such appointment within 30 days after the Interim Decision
Date, then such Neutral, upon the application of either of the Parents shall be
appointed within 10 days of the filing of such application by the Center for
Public Resources, or if such appointment is not so made promptly then promptly
thereafter by the American Arbitration Association in Philadelphia,
Pennsylvania, or if such appointment is not so made promptly then promptly
thereafter by the senior United States District Court judge sitting in
Wilmington, Delaware.  The fees of the Neutral shall be paid equally by the
Parents except that the Neutral shall have discretion to award fees.

     (e)  In consultation with the Neutral, the Parents shall agree upon a
binding schedule and procedure (which procedure may have been previously
discussed under subsection (b)) to be used as a means to resolve or to attempt
to resolve Dispute, with the Neutral making the decision as to the schedule
and/or procedure if the Parents have been unable to agree on any of such matters
within 20 days after the initial selection of the Neutral.  The Parents agree to
participate in a commercially reasonable manner in the procedure to its
conclusion as determined by the Neutral.  If the Parents are not successful in
resolving the Dispute through the procedure described above, then the Parents
agree that (i) the Neutral shall act as the arbitrator in a binding arbitration
in accordance with the American Arbitration Association rules and shall render a
decision and (ii) judgment upon the decision rendered by the Neutral may be
entered in any court having jurisdiction.

     (4)  Continuation of Business.  Notwithstanding the existence of any
Dispute or the pendency of any procedures pursuant to this Appendix B, the
Parents agree and undertake that all payments not in dispute shall continue to
be made and all obligations not in dispute shall continue to be performed.


                                      B-2
<PAGE>
 
                                  Appendix 1
                                  ----------


     (a)  First priority shall be given to maximizing the consistency of the
resolution of the Dispute with the satisfaction of all express obligations of
the Parents and their Affiliates as set forth in the Agreement.

     (b)  Second priority shall be given to resolution of the Dispute in a
manner which best achieves the objectives of the business activities and
arrangements under the Agreement and permits the Parents to realize the benefits
intended to be afforded thereby.

     (c)  Third priority shall be given to such other matters, if any, as the
Parents or the Neutral shall determine to be appropriate under the
circumstances.


                                      B-3