Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER
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 Brigham Exploration Company (the “Company”) on Form 10-Q for the period ending September 30, 2010 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Ben M. Brigham, President, Chief Executive Officer and Chairman of the Board 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 Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

(2)

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

Dated: November 3, 2010		/s/ Ben M. Brigham
		Ben M. Brigham Chief Executive Officer, President and Chairman of the Board

This certification shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934, as amended, and will not be incorporated by reference into any registration statement filed under the Securities Act of 1933, as amended, unless specifically identified therein as being incorporated therein by reference.

A signed original of this written statement required by Section 906, or other document authenticating, acknowledging, or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Brigham Exploration Company and will be retained by Brigham Exploration Company and furnished to the Securities and Exchange Commission or its staff upon request.