Exhibit 23

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

The Board of Directors

Sigma-Aldrich Corporation:

We consent to the incorporation by reference in the registration statement (No. 333 74163) on Form S 3 and registration statements (Nos. 333-49912, 33-24415, 33-62541, 333-64661, 333-30528, and 333 105033) on Form S-8 of Sigma-Aldrich Corporation (the Company) of our report dated February 9, 2010, with respect to the consolidated balance sheets of Sigma-Aldrich Corporation as of December 31, 2009 and 2008, and the related consolidated statements of income, stockholders’ equity, and cash flows for each of the years in the three-year period ended December 31, 2009, and the effectiveness of internal control over financial reporting as of December 31, 2009, which report appears in the December 31, 2009 annual report on Form 10 K of Sigma-Aldrich Corporation.

As discussed in note 10 to the consolidated financial statements, effective January 1, 2007, the Company adopted FASB Interpretation No. 48, Accounting for Uncertainty in Income Taxes, an interpretation of Statement of Financial Accounting Standard No. 109 (ASC 740).

/s/ KPMG

St. Louis, Missouri

February 9, 2010