Sigma Aldrich (SIAL) 10-K 2006 FY Annual report

Exhibit 23

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

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 reports dated February 26, 2007 with respect to the consolidated balance sheets of Sigma-Aldrich Corporation as of December 31, 2006 and 2005, 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, 2006, management’s assessment of the effectiveness of internal control over financial reporting and the effectiveness of internal control over financial reporting as of December 31, 2006, which reports appear in the December 31, 2006 annual report on Form 10-K of Sigma-Aldrich Corporation.

As discussed in Note 1 to the consolidated financial statements, the Company adopted the recognition and disclosure provisions as required by Statement of Financial Accounting Standards No. 158,“Employers’ Accounting for Defined Benefit Pension and Other Postretirement Plans” as of December 31, 2006.

As discussed in Note 12 to the consolidated financial statements, effective January 1, 2006 the Company adopted the fair value method of accounting for stock-based compensation as required by Statement of Financial Accounting Standards No. 123 (Revised 2004),“Share-Based Payment.”

/s/ KPMG LLP

St. Louis, Missouri

February 26, 2007