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                                                                    Exhibit 31.1

                      CERTIFICATION PURSUANT TO SECTION 302
                        OF THE SARBANES-OXLEY ACT OF 2002

I, Robert E. Lee, President and Chief Executive Officer of Millennium Chemicals
Inc., certify that:

1. I have reviewed this Quarterly Report on Form 10-Q of Millennium Chemicals
Inc. for the quarter ended June 30, 2004 as filed with the Securities and
Exchange Commission on August 9, 2004 and as amended by Amendment No. 1 to the
Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission
on August 11, 2004, Amendment No. 2 to the Quarterly Report on Form 10-Q, filed
with the Securities and Exchange Commission on September 23, 2004, and this
Amendment No. 3 to the Quarterly Report on Form 10-Q, filed with the Securities
and Exchange Commission on the date hereof;

2. Based on my knowledge, this quarterly report, as amended, does not contain
any untrue statement of a material fact or omit to state a material fact
necessary to make the statements made, in light of the circumstances under which
such statements were made, not misleading with respect to the period covered by
this quarterly report;

3. [Intentionally Omitted];

4. The registrant's other certifying officer and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have:

         a) designed such disclosure controls and procedures, or caused such
         disclosure controls and procedures to be designed under our
         supervision, to ensure that material information relating to the
         registrant, including its consolidated subsidiaries, is made known to
         us by others within those entities, particularly during the period in
         which this quarterly report is being prepared;

         b) evaluated the effectiveness of the registrant's disclosure controls
         and procedures and presented in this report our conclusions about the
         effectiveness of the disclosure controls and procedures, as of the end
         of the period covered by this report based on such evaluation; and

         c) disclosed in this report any change in the registrant's internal
         control over financial reporting that occurred during the registrant's
         most recent fiscal quarter that has materially affected, or is
         reasonably likely to materially affect, the registrant's internal
         control over financial reporting; and





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5. The registrant's other certifying officer and I have disclosed, based on our
most recent evaluation of internal control over financial reporting, to the
registrant's auditors and the audit committee of the registrant's board of
directors (or persons performing the equivalent functions):

         a) all significant deficiencies and material weaknesses in the design
         or operation of internal controls over financial reporting which are
         reasonably likely to adversely affect the registrant's ability to
         record, process, summarize and report financial information; and

         b) any fraud, whether or not material, that involves management or
         other employees who have a significant role in the registrant's
         internal controls over financial reporting.

Date: September 24, 2004

                                           /s/ ROBERT E. LEE
                                           -------------------------------------
                                           Robert E. Lee
                                           President and Chief Executive Officer
                                           (Principal Executive Officer)