EXHIBIT 5.1 (BAKER BOTTS L.L.P. LETTERHEAD) November 19, 2004 063718.0509 Halliburton Company 1401 McKinney, Suite 2400 Houston, Texas 77010 Ladies and Gentlemen: As set forth in the Registration Statement on Form S-3 (the "Registration Statement") filed by Halliburton Company, a Delaware corporation (the "Company"), with the Securities and Exchange Commission (the "Commission") under the Securities Act of 1933, as amended (the "Act"), relating to the registration under the Act of the offering and sale of $500,000,000 aggregate principal amount of Senior Notes Due 2007 (the "Notes") issued pursuant to an Indenture (the "Indenture") dated as of October 17, 2003 between the Company and JPMorgan Chase Bank, as trustee (the "Trustee"), as supplemented by the Third Supplemental Indenture, dated as of January 26, 2004, that may be sold by the selling securityholders referred to in the Registration Statement from time to time pursuant to Rule 415 under the Act, we are passing upon certain legal matters for the Company in connection with the Notes. At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement. In our capacity as your counsel in connection with the matters referred to above, we have examined originals, or copies certified or otherwise identified, of the Restated Certificate of Incorporation and Bylaws of the Company, each as amended to date, the Indenture, the Notes, corporate records of the Company, including minute books of the Company as furnished to us by the Company, certificates of public officials and of representatives of the Company, statutes and other instruments and documents as a basis for the opinions hereinafter expressed. In giving such opinions, we have relied upon certificates of officers of the Company and of public officials with respect to the accuracy of the material factual matters contained in such certificates. In giving the opinions below, we have assumed that the signatures on all documents examined by us are genuine, that all documents submitted to us as originals are accurate and complete, that all documents submitted to us as copies are true and correct copies of the originals thereof and that all information submitted to us was accurate and complete. In addition, we have assumed that (i) the Indenture has been duly authorized, executed and delivered by the Trustee and constitutes the legal, valid and binding obligation of the Trustee, (ii) the Notes have been duly authenticated by the Trustee and (iii) the Indenture has been validly qualified under the Trust Indenture Act of 1939. BAKER BOTTS L.L.P. Halliburton Company 2 November 19, 2004 On the basis of the foregoing, and subject to the qualifications and limitations hereinafter set forth, we are of the opinion that the Notes constitute legal, valid and binding obligations of the Company, enforceable against the Company, except as the enforceability thereof is subject to the effect of (i) bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer or conveyance or other laws relating to or affecting creditors' rights generally and (ii) general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law). The opinion set forth above is limited in all respects to (1) matters of the laws of the State of New York, (2) the General Corporation Law of the State of Delaware, which includes the statutory provisions and also all applicable provisions of the Delaware Constitution and reported judicial decisions interpreting these laws, and (3) applicable federal law. We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our Firm under the heading "Legal Matters" in the prospectus forming a part of the Registration Statement. In giving such consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission thereunder. Very truly yours, BAKER BOTTS L.L.P. DWT/JDS