Exhibit 99.1

[LETTERHEAD OF CITIGROUP GLOBAL MARKETS INC.]

The Board of Directors

Lyondell Chemical Company

One Houston Center, Suite 700

1221 McKinney Street

Houston, Texas 77010

Members of the Board:

We hereby consent to the inclusion of our opinion letter as Annex B to, and to the reference thereto under the captions “SUMMARY — Opinion of Citigroup Global Markets Inc., Lyondell’s Financial Advisor” and “PROPOSALS TO APPROVE THE PROPOSED TRANSACTION — Opinion of Citigroup Global Markets Inc., Lyondell’s Financial Advisor” in, the Joint Proxy Statement/Prospectus of Lyondell Chemical Company (“Lyondell”) and Millennium Chemicals Inc. (“Millennium”) relating to the proposed merger involving Lyondell and Millennium, which Joint Proxy Statement/Prospectus forms a part of the Registration Statement on Form S-4 of Lyondell. By giving such consent, we do not thereby admit that we are experts with respect to any part of such Registration Statement within the meaning of the term “expert” as used in, or that we come within the category of persons whose consent is required under, the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

/S/ CITIGROUP GLOBAL MARKETS INC.

CITIGROUP GLOBAL MARKETS INC.

April 26, 2004