Exhibit 99.1



                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


In connection with the Quarterly  Report of Halliburton  Company (the "Company")
on Form 10-Q for the period  ending June 30,  2002 as filed with the  Securities
and Exchange  Commission on the date hereof (the  "Report"),  I, David J. Lesar,
Chief Executive Officer of the  Company, certify, pursuant to  18 U.S.C. Section
1350, as  adopted pursuant to  Section 906 of  the Sarbanes-Oxley  Act of  2002,
that:

    (1)  The Report  fully complies  with the  requirements of  section 13(a) or
         15(d) of the Securities Act of 1934; and

    (2)  The  information  contained  in  the  Report fairly  presents,  in  all
         material respects, the financial condition and results of operations of
         the Company.



    /s/ David J. Lesar
    --------------------------------
    David J. Lesar
    Chief Executive Officer
    August 13, 2002