Exhibit 23.1

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

The Board of Directors

Brigham Exploration Company:

We consent to the incorporation by reference in the registration statements on Form S-8 (Nos. 333-56961, 333-70137, 333-135073, and 333-135028) and on Form S-3 (Nos. 333-116390, 333-131881, and 333-136150) of Brigham Exploration Company of our reports dated March 6, 2007, with respect to the consolidated balance sheet of Brigham Exploration Company as of December 31, 2006, and the related consolidated statements of operations, stockholders’ equity, and cash flows for the year ended, management’s assessment of the effectiveness of internal controls over financial reporting as of December 31, 2006, which reports appear in the December 31, 2006 annual report on Form 10-K of Brigham Exploration Company. As discussed in Note 1 to the consolidated financial statements, effective January 1, 2006, the Company adopted the provisions of Statement of Financial Accounting Standards No. 123 (revised 2004), Share Based Payment.

KPMG LLP

Dallas, Texas

March 6, 2007