Exhibit 8.2

[Letterhead of Weil, Gotshal & Manges LLP]

June 18, 2004

Board of Directors

Millennium Chemicals Inc.

20 Wight Avenue, Suite 100

Hunt Valley, MD 21030

Ladies & Gentlemen:

You have requested our opinion regarding certain federal income tax consequences of the merger (the “Merger”) of Millennium Subsidiary LLC (“Merger Sub”), a Delaware limited liability company and a direct wholly-owned subsidiary of Millennium Chemicals Inc. (“Millennium”), a Delaware corporation, with and into Millennium.

In formulating our opinion, we examined such documents as we deemed appropriate, including the Agreement and Plan of Merger dated as of March 28, 2004 by and among Lyondell Chemical Company (“Lyondell”), a Delaware corporation, Millennium and Merger Sub (the “Merger Agreement”) and the Registration Statement on Form S-4, initially filed by Lyondell with the Securities and Exchange Commission on April 26, 2004 (Registration No. 333-114877), as amended (with all amendments thereto, the “Registration Statement”). In addition, we have obtained such additional information as we deemed relevant and necessary through consultation with various officers and representatives of Lyondell and Millennium. Any capitalized terms used but not defined herein have the meaning given to such terms in the Merger Agreement and the Registration Statement.

Our opinion set forth below assumes (1) the accuracy of the statements and facts concerning the Merger set forth in the Merger Agreement and the Registration Statement and (2) the consummation of the Merger in the manner contemplated by, and in accordance with the terms set forth in, the Merger Agreement and the Registration Statement.

Board of Directors, Millenium Chemicals Inc.

June 18, 2004

Page 2

Based upon the facts and statements set forth above, our examination and review of the documents referred to above and subject to the assumptions set forth above and qualifications set forth below, we hereby confirm, as of the date hereof, the opinion of Weil, Gotshal & Manges LLP which is attributed to us in the Registration Statement under the heading “PROPOSALS TO APPROVE THE PROPOSED TRANSACTION—Material U.S. Federal Income Tax Consequences of the Proposed Transaction,” insofar as it constitutes statements of law or legal conclusions and except to the extent qualified therein.

Our opinion is based on current provisions of the Code, the Treasury Regulations promulgated thereunder, published pronouncements of the Internal Revenue Service and case law, any of which may be changed at any time with retroactive effect. Any change in applicable laws or facts and circumstances surrounding the Merger, or any inaccuracy in the statements, facts, assumptions and representations on which we have relied, may affect the continuing validity of the opinion set forth herein. We assume no responsibility to inform you of any such change or inaccuracy that may occur or come to our attention. No opinion is expressed on any matter other than those specifically covered by the foregoing opinion.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and the reference to our firm therein under the headings “QUESTIONS AND ANSWERS ABOUT THE PROPOSED TRANSACTION,” “PROPOSALS TO APPROVE THE PROPOSED TRANSACTION—Material U.S. Federal Income Tax Consequences of the Proposed Transaction” and “LEGAL MATTERS.” This opinion is rendered solely for your benefit in connection with the transactions described above.

Very truly yours,

/s/ Weil, Gotshal & Manges LLP