AMENDMENT NO. 2 TO CREDIT AGREEMENT

Exhibit 4.6(b)

AMENDMENT NO. 2

TO CREDIT AGREEMENT

AMENDMENT (this “Amendment”) dated as of September 29, 2006 to the Credit Agreement dated as of August 16, 2006 (as amended, the “Credit Agreement”) among LYONDELL CHEMICAL COMPANY, a Delaware corporation, and the AGENTS and LENDERS from time to time party thereto.

The parties hereto agree as follows:

SECTION 1. Defined Terms; References. Unless otherwise specifically defined herein, each term used herein which is defined in the Credit Agreement has the meaning assigned to such term in the Credit Agreement. 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 Credit Agreement, and each reference to “the Credit Agreement” “thereof”, “thereunder”, “therein” and “thereby” and each other similar reference to the Credit Agreement contained in any Loan Document shall, after this Amendment becomes effective, refer to the Credit Agreement as amended hereby.

SECTION 2. Increase in Revolving Commitments. (a) With effect from and including the date hereof, (i) each Person listed on the signature pages hereof which is not a party to the Credit Agreement (a “New Lender”) shall become a Revolving Lender party to the Credit Agreement, (ii) the Revolving Commitment of each Revolving Lender shall be the applicable amount set forth opposite the name of such Lender on the attached Commitment Schedule, which shall become the Commitment Schedule referred to in the Credit Agreement and (iii) the participating interests of the respective Revolving Lenders in all outstanding Letters of Credit shall be redetermined on the basis of the Revolving Commitments after giving effect to (i) and (ii) above.

(b) The definition of “Revolving Commitment” is amended by the addition of the following concluding sentence:

The aggregate amount of the Revolving Commitments as of September 29, 2006 is $1,055,000,000.

SECTION 3. Reduction In Term Loan Pricing. (a) Part B of the definition of “Applicable Margin” is amended to read as follows:

B. Initial Term Loans. The Applicable Margin for Euro-Dollar Initial Term Loans and Base Rate Initial Term Loans for any day are the respective percentages set forth in the chart below in the applicable row and column based upon the Status that exists on such day; provided that in the event any Incremental Term Loans are borrowed with Applicable Margins which exceed those specified above by more than

0.25% per annum, the Applicable Margin for the Initial Term Loans shall be increased so as to be exactly 0.25% per annum less than the Applicable Margins applicable to such Incremental Term Loans. For this purpose, front-end fees or original issue discount with respect to Incremental Term Loans shall be equated to additional margin on the basis of an assumed four-year average life to maturity (i.e., 1.00% in front-end fees and/or original issue discount equals 0.25% additional margin).

(b) The following new definitions are added to Section 1.01 of the Credit Agreement in appropriate alphabetical position:

“Level A Status” exists at any date if, at such date, the Total Leverage Ratio is less than 3.00 to 1.00.

“Level B Status” exists at any date if, at such date, the Total Leverage Ratio is equal to or greater than 3.00 to 1.00.

(c) The following definition is amended to read in its entirety as follows:

“Status” refers to the determination of which of (i) Level I Status, Level II Status, Level III Status or Level IV Status or (ii) Level A Status or Level B Status, respectively, exists at any date.

SECTION 4. Miscellaneous. The definition of “Lyondell-Equistar Debt” is amended to read in its entirety as follows:

“Lyondell-Equistar Debt” means Debt under the 7.55% Notes Due 2026 issued by the Borrower pursuant to an Indenture dated as of January 29, 1996 between the Borrower and Texas Commerce Bank National Association, as trustee, as supplemented by the First Supplemental Indenture dated as of February 15, 1996 and the Second Supplemental Indenture dated as of December 1, 1997, which Debt has been assumed by Equistar and with respect to which, as between the Borrower and Equistar, Equistar is the obligor and the Borrower is the guarantor.

SECTION 5. Representations of Borrower. The Borrower represents and warrants that (i) the representations and warranties of the Borrower set forth in Article 4 of the Credit Agreement are true in all material respects on and as of date hereof with the same effect as though made on and as of such date, except to

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the extent such representations and warranties expressly relate to an earlier date and (ii) no Default has occurred and is continuing on such date.

SECTION 6. Governing Law. This Amendment shall be governed by and construed in accordance with the laws of the State of New York.

SECTION 7. 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 8. Effectiveness. This Amendment shall become effective as of the date hereof when each of the following conditions shall have been satisfied:

(a) receipt by the Administrative Agent of counterparts hereof signed by each of the parties listed on the signature pages hereof (or, in the case of any party as to which an executed counterpart shall not have been received, the Administrative 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);

(b) receipt by the Administrative Agent of an opinion of such counsel for the Borrower as may be acceptable to the Administrative Agent, substantially to the effect of Exhibits B and C to the Credit Agreement with reference to this Amendment and the Credit Agreement as amended hereby;

(c) receipt by the Administrative Agent of all documents it may reasonably request relating to the existence of the Borrower, the corporate authority for and the validity of the Credit Agreement as amended hereby, and any other matters relevant hereto, all in form and substance satisfactory to the Administrative Agent.

The Administrative Agent shall promptly notify the Borrower and the Lenders of the effectiveness of this Amendment, 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.

COMMITMENT SCHEDULE