AMENDMENT NO. 5 TO UNDERTAKING AGREEMENT

Exhibit 4.23(e)

AMENDMENT NO. 5 TO UNDERTAKING AGREEMENT

AMENDMENT dated as of November 15, 2006 to the Undertaking Agreement dated as of December 17, 2003 (as heretofore amended, the “Undertaking Agreement”) by LYONDELL CHEMICAL COMPANY, a Delaware corporation (“Lyondell”), in favor of the PURCHASERS (as defined in the Receivables Purchase Agreement dated as of December 17, 2003 (as amended, the “Receivables Agreement”) among Lyondell Funding II, LLC, as Seller, Lyondell, as Servicer, the Purchasers from time to time party thereto and Citicorp USA, Inc., as asset agent and administrative agent (the “Agent”) for the Purchasers) and CITICORP USA, INC., as Agent.

The parties hereto agree to amend the Undertaking Agreement as follows:

Section 1. Defined Terms; References. Unless otherwise specifically defined herein, each term used herein which is defined in the Undertaking Agreement, or incorporated by reference therein, has the meaning assigned to such term in the Undertaking Agreement or so incorporated. Each reference to “hereof”, “hereunder”, “herein” and “hereby” and each other similar reference and each reference to “this Agreement” and each other similar reference contained in the Undertaking Agreement shall, after this Amendment becomes effective, refer to the Undertaking Agreement as amended hereby.

Section 2. Amendments. (a) Section 1.01 is amended by inserting the following definitions therein in their appropriate alphabetical positions:

“LCR Acquisition” means the acquisition, directly or indirectly, by Lyondell of the 41.25% equity interest in LCR which, immediately prior to the Closing Date, was not owned by it.

“No Less Favorable” means, for purposes of comparing the terms and conditions of a given debt instrument with those of another debt instrument or instruments, that the terms and conditions of the former are no less favorable to Lyondell, taken as a whole, than the terms and conditions of the latter (except that the interest rate and similar terms applicable to the former shall be at the prevailing market rates at the time of issuance or, if debt securities issued thereunder are to be fungible with debt securities previously issued, rates that, taken together with the sales price of such securities, reflect then prevailing market rates).

“Series E Senior Secured Note Indenture” means the Series E Senior Note Indenture dated as of May 20, 2003 among Lyondell, the subsidiary guarantors party thereto and The Bank of New York, as trustee, pursuant to which Lyondell issued the 10.5% Senior Notes Due 2013.

(b) The following definitions in Section 1.01 are amended to read in their entirety as follows:

“Additional JV Debt” means Indebtedness incurred by Equistar after August 16, 2006 in connection with the admission into such Lyondell Joint Venture of a new partner or member, as the case may be; provided that, at the time such Indebtedness is incurred, such Lyondell Joint Venture’s ratio of Indebtedness to EBITDA, calculated on a pro forma basis (without giving effect to anticipated expense reductions or other synergies) for its then most recent fiscal year for which financial statements are available, does not exceed 2.25:1.00.

“Adjusted EBITDA” means, for any period, the sum of (i) the EBITDA of the Non-JV Group for such period, adjusted to exclude the effect of one time charges incurred by the Non-JV Group in connection with (A) a TDI Sale, (B) the payment required to be made by LCR in connection with the LCR Acquisition upon the termination of the crude oil supply agreement to which it is a party, in an aggregate amount not exceeding $176,250,000 and (C) other cash restructuring charges in an aggregate amount not exceeding $50,000,000, plus (ii) the Distributed Cash Flow of all Lyondell Joint Ventures and non-wholly owned Subject Assets Transferees for such period.

“Asset Sale” means any sale, lease or other disposition (including any such transaction effected by way of merger or consolidation) by Lyondell or any of its Subsidiaries of any asset, including without limitation any sale-leaseback transaction, whether or not involving a capital lease, but excluding (i) dispositions of inventory or equipment in the ordinary course of business, (ii) dispositions of Temporary Cash Investments and cash payments otherwise permitted under this Agreement (including Restricted Payments permitted by Section 3.12), (iii) dispositions to Lyondell or a Subsidiary of Lyondell, (iv) leases of real property owned by LCR in the ordinary course of business, (v) dispositions constituting Investments permitted by Section 3.13 (except as provided below) and (v) dispositions constituting Liens permitted by Section 3.08. For avoidance of doubt, a Securitization Transaction constitutes an Asset Sale and does not, in itself, give rise to an obligation secured by a Lien on an asset of Lyondell or a Subsidiary. To the extent that, in connection with (x) an Investment by Lyondell or a Subsidiary in a Lyondell Joint Venture or (y) a reduction in the proportionate interest of Lyondell or a Subsidiary in a Lyondell Joint Venture, Lyondell or a Subsidiary receives net cash proceeds (determined as if such transaction were an Asset Sale), then such transaction shall be treated as an Asset Sale to the extent of such net cash proceeds.

“Equity Issuance” means any issuance of (a) equity securities (including any preferred equity securities) by Lyondell, other than (i)

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equity securities issued to a Subsidiary, (ii) equity securities issued pursuant to employee benefit and/or dividend reinvestment plans in the ordinary course of business and (iii) equity securities issued as consideration for a Business Acquisition or (b) an Equity Equivalent.

“Senior Notes” means notes of Lyondell which (i) mature no earlier than November 17, 2007 and (ii) contain otherwise substantially the same terms and conditions as the Senior Secured Note Indentures (or, in the case of any such notes issued after the Closing Date, terms and conditions that are No Less Favorable than the Senior Secured Note Indentures). As of August 16, 2006, the Senior Notes consist of the notes issued under the Senior Secured Note Indentures.

“Senior Secured Note Indentures” means, collectively, the Series A Senior Secured Note Indenture, the Series C Senior Secured Note Indenture, the Series D Senior Secured Note Indenture and the Series E Senior Secured Note Indenture.

(c) The following definitions in Section 1.01 are deleted: Capital Expenditures; LMC; Permitted LCR Acquisition; Permitted LCR Sale; PO-11 JV and PO-12 JV; Series B Senior Secured Note Indenture; Specified Business Acquisition; and 2003 Indenture.

(d) Section 1.02(c) is amended to read as follows:

(c) In the event of any future material acquisition or disposition of assets by Lyondell and its Consolidated Subsidiaries (other than a TDI Sale and the TDI Restructuring), determinations of Adjusted EBITDA for purposes of Section 3.11 shall be made on a pro forma basis as if such transaction had been consummated on the first day of such period.

(e) Section 3.08(a) is amended to read as follows:

(a) Liens existing on August 16, 2006 securing Indebtedness in an aggregate principal amount not exceeding $75,000,000;

(f) Section 3.08(j) is amended by changing the figure “$50,000,000” appearing therein to “$75,000,000”.

(g) Section 3.09(b) is amended to read as follows:

(b) the Indebtedness of such Subsidiary outstanding on August 16, 2006; and refinancings thereof provided that the principal amount thereof is not increased beyond the amount outstanding thereunder on August 16, 2006 and the amount of any refinancing costs;

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(h) Section 3.09(f) is amended by adding the word “and” at the end thereof.

(i) Section 3.09(g) is amended by changing the figure “$50,000,000” appearing therein to “$75,000,000” and by deleting the word “and” at the end thereof.

(j) Section 3.09(h) is deleted.

(k) Section 3.12(a) is amended to read as follows:

(a) Neither Lyondell nor any Subsidiary will declare or make any Restricted Payment; provided that (i) so long as at the time no Potential Event of Termination or Event of Termination shall exist, Lyondell may pay regular quarterly dividends on its common stock at a rate not exceeding $0.225 per share per quarter (adjusted to reflect any stock split, stock dividend, stock combination or similar transaction subsequent to June 27, 2002) and (ii) Lyondell may pay any such dividend within 60 days of declaration thereof if no Event of Termination or Potential Event of Termination existed at the date of such declaration.

(l) Section 3.13 is amended to read as follows:

Section 3.13. Investments: Business Acquisitions. Neither Lyondell nor any Subsidiary will make or acquire any Investment in any Person or make any Business Acquisition other than:

(a) Investments in Lyondell and its Subsidiaries;

(b) Investments in Lyondell Joint Ventures (including any such Investments that would constitute a Business Acquisition) to the extent permitted by Section 3.19;

(c) Temporary Cash Investments;

(d) employee Loans and advances for travel, entertainment, relocation and other ordinary business expenses;

(e) Business Acquisitions (other than Investments in Lyondell Joint Ventures);

(f) Investments consisting of notes and equity securities received as consideration for Asset Sales, to the extent permitted by the last sentence of Section 3.07; and

(g) Investments (other than Investments in Lyondell Joint Ventures) made after August 16, 2006 if, immediately after such Investment is made or acquired (i) the aggregate net book value of all Investments permitted by this clause (i) does not exceed $50,000,000, or (ii) the Compliance Test would be satisfied.

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For avoidance of doubt, if Lyondell makes a Business Acquisition with intention, promptly executed, that the assets so acquired be contributed to a Lyondell Joint Venture, such transaction is an Investment permitted by Section 3.13(b), subject to the limitations specified in Section 3.19, and is not to be included in computations of compliance with Section 3.13(e) or (g).

(m) Section 3.14 is amended to read as follows:

Section 3.14. Transactions with Affiliates. Lyondell will not, and will not permit any Subsidiary to, directly or indirectly, (a) pay any funds to or for the account of any Affiliate, (b) make any investment in any Affiliate (whether by acquisition of stock or indebtedness, by loan, advance, transfer of property, guarantee or other agreement to pay, purchase or service, directly or indirectly, any Indebtedness, or otherwise), (c) lease, sell, transfer or otherwise dispose of any assets, tangible or intangible, to any Affiliate, or (d) participate in, or effect, any transaction with any Affiliate, except on a basis no less favorable to the Company and its Subsidiaries than could be obtained on an arms-length basis; provided that the foregoing provisions of this Section shall not prohibit (i) any Restricted Payment permitted by Section 3.12, (ii) any Subsidiary from declaring or paying any lawful dividend or other payment ratably in respect of all its capital stock of the relevant class or on a basis more favorable to a Transaction Party, or (iii) Lyondell from issuing shares of its common stock upon conversion of Millennium’s 4.000% Convertible Debentures due 2023. It is understood that the agreements set forth in Schedule 3.16 do not contravene this Section.

(n) Section 3.15 is amended to read as follows:

Section 3.15. Limitation on Restrictions Affecting Subsidiaries. Neither Lyondell nor any of its Subsidiaries will enter into, or suffer to exist, any agreement with any Person which prohibits or limits the ability of any Subsidiary to (a) pay dividends or make other distributions or pay any Indebtedness owed to Lyondell or any Subsidiary, (b) make loans or advances to Lyondell or any Subsidiary, (c) transfer any of its properties or assets to Lyondell or any Subsidiary, (d) create, incur, assume or suffer to exist any Lien upon any of its property, assets or revenues, whether now owned or hereafter acquired, (e) Guarantee any Indebtedness of Lyondell or another Subsidiary or (f) suffer to exist any Lien on capital stock or other equity interests issued by it; provided that the following shall be permitted: (i) the CA Loan Documents; (ii) the agreements governing (x) the Indebtedness of Lyondell and its Subsidiaries outstanding on August 16, 2006 or (y) Securitization Transactions entered into by Lyondell and

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its Subsidiaries prior to August 16, 2006, in each case as in effect on August 16, 2006 (the “Existing Restrictions”) and the agreements governing Indebtedness or Securitization Transactions incurred or entered into after August 16, 2006 and containing limitations No Less Favorable than the Existing Restrictions; (iii) agreements between a JV Subsidiary and another partner or member of Lyondell Joint Venture of which such JV Subsidiary is a partner or member so long as the limitations imposed thereby are not materially more restrictive than those contained in agreements set forth in Schedule 3.16; (iv) agreements with respect to Indebtedness secured by Liens permitted under Section 3.08(b) – (e) containing restrictions on the ability to transfer or grant Liens on the assets securing such Indebtedness; (v) customary restrictions contained in stock purchase agreements, asset sale agreements limiting the transfer of assets pending the closing of the sale and customary non-assignment provisions in leases and other contracts entered into in the ordinary course of business; (vi) the PBGC Settlement Agreement; (vii) agreements entered into in connection with Indebtedness incurred by Lyondell containing limitations No Less Favorable than the Senior Notes or the Senior Subordinated Notes as in effect on August 16, 2006; (viii) restrictions existing on the Closing Date on POSM and any Subsidiary whose only significant assets are partnership interests in POSM; (ix) customary limitations on the activities of a Special Purpose Subsidiary, including limitations set forth in the Transaction Documents; and (x) agreements between Lyondell or a non-wholly owned Subject Assets Transferee and the Acquiring Person (or an Affiliate thereof) of an interest in such non-wholly owned Subject Assets Transferee so long as the limitations imposed thereby are not materially more restrictive than those contained in the agreements set forth in Schedule 3.16; and provided further that (x) clauses (c) and (d) above shall be inapplicable to any Foreign Subsidiary or other Subsidiary conducting substantially all its operations outside the United States, (y) clauses (c), (d) and (e) shall be inapplicable to any Subject Assets Transferee and (z) from and after the Investment Grade Date, clause (d) shall be inapplicable to Lyondell or any other Subsidiary.

(o) Section 3.16 is amended to read as follows:

Section 3.16. Restrictions on Lyondell Joint Ventures. Lyondell shall use its best efforts, including, without limitation, by voting (through the JV Subsidiaries) its indirect interest in any Lyondell Joint Venture at any meetings of the respective governing bodies of such Lyondell Joint Venture, to:

(a) maintain without material change the cash distribution policy of Equistar as stated in the Equistar Partnership Agreement as in effect on the Closing Date;

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(b) limit the Indebtedness that Equistar creates, incurs, assumes or permits to exist (exclusive of Indebtedness owing to Lyondell or a Subsidiary) to an aggregate outstanding principal amount which, together with all other outstanding Indebtedness of such Lyondell Joint Venture, does not exceed $3,100,000,000 plus the amount of any Additional JV Debt;

(c) prevent Equistar from, directly or indirectly, entering into, incurring or permitting to exist any agreement or other arrangement with any Person that prohibits, restricts or imposes any condition upon the ability of such Lyondell Joint Venture to pay dividends or other distributions to, or to make or repay loans or advances to, Lyondell or any JV Subsidiary, which restrictions or conditions are materially more restrictive than those contained in agreements to which such Lyondell Joint Venture is a party set forth in Schedule 3.16, as in effect on the Closing Date; and

(d) cause one or more JV Subsidiaries to retain the material rights (or the right to reacquire the material rights) of Lyondell LP4 Inc. (formerly Lyondell Petrochemical G.P. Inc.) under the Equistar Partnership Agreement.

(p) Section 3.17 is deleted and replaced by “[Reserved]”.

(q) Section 3.19 is amended (i) by changing the date “July 1, 2004” to “July 1, 2006” in two places and (ii) by revising clause (iv) of the proviso thereto to read “(iv) the LCR Acquisition will not be subject to the restrictions of this Section.”

Section 3. Representations of Lyondell. Lyondell represents and warrants that (i) the representations and warranties of Lyondell set forth in Article 2 of the Undertaking Agreement and Article IV of the Receivables Agreement will be true in all material respects on and as of the Amendment Effective Date (as defined below) with the same effect as though made on and as of such date, except to the extent such representations and warranties expressly relate to an earlier date and (ii) no Potential Event of Termination or Event of Termination will have occurred and be continuing on such date.

Section 4. Governing Law. This Amendment shall be governed by and construed in accordance with the laws of the State of New York.

Section 5. Counterparts. This Amendment may be signed in any number of counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

Section 6. Effectiveness. This Amendment shall become effective on the date (the “Amendment Effective Date”) when the Agent shall have received counterparts hereof signed by each of the Required Purchasers and Lyondell (or,

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in the case of any party as to which an executed counterpart shall not have been received, the Agent shall have received in form satisfactory to it facsimile or other written confirmation from such party of execution of a counterpart hereof by such party). Promptly after the Amendment Effective Date occurs, the Agent shall notify Lyondell and the Purchasers thereof, and such notice shall be conclusive and binding on all parties hereto.

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

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