Filed pursuant to Rule 424(b)(3)
                                                     Registration No. 333-110035

Prospectus Supplement
(To Prospectus Dated February 9, 2004)


                                 $1,200,000,000
                               HALLIBURTON COMPANY
                3-1/8% CONVERTIBLE SENIOR NOTES DUE JULY 15, 2023
                                       AND
               COMMON STOCK ISSUABLE UPON CONVERSION OF THE NOTES
                           
                              --------------------

         This document supplements the prospectus dated February 9, 2004,
relating to $1,200,000,000 aggregate principal amount of our 3-1/8% Convertible
Senior Notes due July 15, 2023 and the shares of common stock issuable upon
conversion of the notes. You should read this prospectus supplement in
conjunction with the accompanying prospectus, which is to be delivered by
selling securityholders to purchasers along with this prospectus supplement.

         Our common stock is listed on the New York Stock Exchange under the
symbol "HAL." On December 17, 2004, the closing price for our common stock on
the New York Stock Exchange was $39.24 per share.

         INVESTING IN THE NOTES AND THE COMMON STOCK ISSUABLE UPON THEIR
CONVERSION INVOLVES RISKS. SEE "RISK FACTORS" BEGINNING ON PAGE 12 OF THE
PROSPECTUS.

         NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED WHETHER
THIS PROSPECTUS IS TRUTHFUL OR COMPLETE. ANY REPRESENTATION TO THE CONTRARY IS A
CRIMINAL OFFENSE.

         On December 17, 2004, we entered into a supplemental indenture with the
trustee in which we eliminated our right to settle the conversion of the notes
solely in shares of our common stock. The supplemental indenture does not modify
your rights as a holder of the notes. We have provided below revisions to
certain paragraphs of the "Conversion of Notes" section of the prospectus which
reflect changes under the supplemental indenture.

         We believe that the modifications to the terms of the notes caused by
the supplemental indenture will not constitute an exchange for federal income
tax purposes, and therefore that there will be no federal income tax
consequences to holders of the notes as a result of any such modifications.
Holders should refer to the discussion in the prospectus under the heading
"Material United States Federal Income Tax Consequences" for a summary of the
United States federal income tax consequences relevant to holders of the notes.

         The information in the third paragraph on the cover page of the
prospectus is replaced and superseded by the following:

                  "The notes will mature on July 15, 2023. Holders may convert
         the notes into cash or a combination of cash and shares of our common
         stock (unless earlier redeemed or repurchased by us) under the
         following circumstances: (1) if the price of our common stock issuable
         upon conversion of the notes reaches specified thresholds described in
         this prospectus, (2) if we call the notes for redemption, (3) upon the
         occurrence of specified corporate transactions described in this
         prospectus or (4) if the credit ratings assigned to the notes decline
         below the levels described in this prospectus. Upon conversion, we will
         have the right to satisfy all or a portion of our conversion obligation
         in cash or a combination of cash and common stock. In no event shall
         the cash amount we use to satisfy all or a portion of our conversion
         obligation be less than the aggregate principal amount of the notes
         being converted. The initial conversion 


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         rate is 26.5583 shares of common stock per each $1,000 principal amount
         of notes. This is equivalent to an initial conversion price of $37.65
         per share."

         The information in the second and third paragraphs under the caption
"Summary--The Offering--Conversion Rights" on page 6 of the prospectus is
replaced and superseded by the following:

                  "For each $1,000 principal amount of notes surrendered for
         conversion, you initially will be entitled to receive cash or a
         combination of cash and stock with a value equivalent to 26.5583 shares
         of our common stock. This represents an initial conversion price of
         $37.65 per share of common stock. As described in this prospectus, the
         conversion rate may be adjusted for certain reasons. Except as
         otherwise described in this prospectus, you will not receive any cash
         payment representing accrued and unpaid interest upon conversion of a
         note; however, we will continue to pay additional amounts, if any, on
         the notes and the common stock issuable upon conversion thereof to the
         holder in accordance with the registration rights agreement. Notes
         called for redemption may be surrendered for conversion prior to the
         close of business on the business day immediately preceding the
         redemption date.

                  Upon conversion, we will have the right to satisfy all or a
         portion of our conversion obligation in cash or a combination of cash
         and common stock. In no event shall the cash amount we use to satisfy
         all or a portion of our conversion obligation be less than the
         aggregate principal amount of the notes being converted."

         The information in the second and third paragraphs under the caption
"Description of Notes--Conversion of Notes" beginning on page 44 of the
prospectus is replaced and superseded by the following:

                  "Except as otherwise described below, you will not receive any
         cash payment representing accrued and unpaid interest (including
         contingent interest, if any) upon conversion of a note and we will not
         adjust the conversion rate to account for the accrued and unpaid
         interest. Upon conversion of a note, we will become obligated to
         deliver to you cash or a combination of cash and shares of common
         stock, together with any cash payment for fractional shares (the
         "conversion obligation"). Delivery of cash or a combination of cash and
         shares of common stock and any cash payment for fractional shares will
         be deemed to satisfy our obligation to pay the principal amount of the
         notes, including accrued and unpaid interest (including contingent
         interest, if any). Accrued and unpaid interest (including contingent
         interest, if any) will be deemed paid in full rather than canceled,
         extinguished or forfeited. The trustee will initially act as the
         conversion agent. Notwithstanding conversion of any notes, the holders
         of the notes and any common stock issuable upon conversion thereof will
         continue to be entitled to receive additional amounts in accordance
         with the registration rights agreement. See "Registration Rights
         Agreement.""

         The information under the caption "Description of Notes--Conversion of
Notes--Payment Upon Conversion--Conversion on or Prior to the Final Notice Date"
beginning on page 46 of the prospectus is replaced and superseded by the
following:

                  "Upon conversion, we will satisfy our conversion obligation by
         delivering to you either (1) cash or (2) a combination of cash and
         shares of our common stock, as follows:

                           (1) Cash Settlement. If we elect to satisfy the
                  entire conversion obligation in cash, then we will deliver to
                  you an amount in cash equal to the product of:

                               o   a number equal to (1) the aggregate principal
                                   amount of notes to be converted divided by
                                   1,000 multiplied by (2) the applicable
                                   conversion rate and

                               o   the average closing price of our common stock
                                   during the cash settlement averaging period
                                   (as described below).

                           (2) Combined Settlement. If we elect to satisfy a
                  portion of the conversion obligation in cash (the "partial
                  cash amount") and a portion in shares of our common stock,
                  then we will deliver 


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                  to you such partial cash amount, plus a number of full shares
                  equal to the greater of (1) one and (2) the excess, if any,
                  of:

                               o   a number of shares equal to (i) the aggregate
                                   principal amount of notes to be converted
                                   divided by 1,000, multiplied by (ii) the
                                   applicable conversion rate, over

                               o   the number of shares equal to the sum, for
                                   each day of the cash settlement averaging
                                   period, of (x) 10% of the partial cash
                                   amount, divided by (y) the closing price of
                                   our common stock on such day.

                  Cash will be paid in lieu of any fractional shares. In no
                  event shall the partial cash amount be less than the aggregate
                  principal amount of the notes being converted.

                  In the event that we receive your notice of conversion on or
         prior to the day that is 20 days prior to maturity (the "final notice
         date"), the following procedures will apply: we will notify you,
         through the trustee, of the dollar amount to be satisfied in cash
         (which must be expressed either as 100% of the conversion obligation or
         as a fixed dollar amount) at any time on or before the date that is
         three business days following receipt of your notice of conversion
         ("cash settlement notice period"). You may retract the conversion
         notice at any time during the two business day period beginning on the
         day after the final day of the cash settlement notice period
         ("conversion retraction period"). If you have not retracted your
         conversion notice during the conversion retraction period, then cash
         settlement or combined settlement of cash and shares of common stock
         will occur on the business day following the final day of the 10 New
         York Stock Exchange trading day period beginning on the day after the
         final day of the conversion retraction period (the "cash settlement
         averaging period")."

           The date of this prospectus supplement is December 20, 2004


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