Exhibit 8.1

October 25, 2010   Sigma-Aldrich Corporation 3050 Spruce Street St. Louis, Missouri 63103   Re:     Sigma-Aldrich Corporation  Registration Statement on Form S-3   To the Board of Directors:   We have acted as special counsel to Sigma-Aldrich Corporation, a Delaware corporation (“Sigma-Aldrich”), in connection with the proposed issuance of up to $300,000,000 aggregate principal amount of 3.375% Notes due November 1, 2020 (the “Notes”) pursuant to the Prospectus Supplement dated October 25, 2010 (“Prospectus Supplement”) to the Prospectus (the “Prospectus”) contained in Sigma-Aldrich’s Registration Statement on Form S-3 (File No. 333-170109) (the “S-3 Registration Statement”) filed by Sigma-Aldrich under the Securities Act of 1933, as amended. The Notes are being issued under an Indenture (the “Indenture”), between Sigma-Aldrich and Deutsche Bank Trust Company Americas, as trustee. Unless otherwise indicated, each defined term has the meaning ascribed to it in the S-3 Registration Statement.   In connection with this opinion, we have examined and are familiar with originals and copies, certified or otherwise identified to our satisfaction, of the (i) the S-3 Registration Statement, (ii) the Prospectus and Prospectus Supplement, (iii) the Indenture, and (vi) such other documents as we have deemed necessary or appropriate in order to enable us to render this opinion.   In rendering our opinion, we have assumed, with your permission, that (i) the final executed version of the Indenture will be identical in all material respects to the version most recently supplied to us and that such final version will be valid and enforceable in accordance with its terms, (ii) the information set forth in the S-3 Registration Statement, the Prospectus, the Prospectus Supplement and the Indenture is true, complete and correct, and (iii) the legal capacity of each natural person, the genuineness of all signatures, the authenticity of all documents submitted to us as originals, and the conformity to original documents of all documents submitted to us as copies or drafts. We have assumed without independent verification that the factual information set forth in the Prospectus and Prospectus Supplement relating to the Notes and the offering of the Notes is accurate and complete in all material respects, and our opinion is conditioned expressly on, among other things, the accuracy as of the date hereof, and the continuing accuracy, of all of such factual information through and as of the date of issuance of the Notes. Any material changes in the facts referred to, set forth or assumed herein or in the Prospectus or Prospectus Supplement may affect the conclusions stated herein.

Sigma-Aldrich Corporation

October 25, 2010

Page 2

In addition, in rendering our opinion, we have considered the applicable provisions of (a) the Internal Revenue Code of 1986 as in effect on the date hereof (the “Code”), (b) the applicable Treasury Regulations as in effect on the date hereof (the “Regulations”), (c) current administrative interpretations by the Internal Revenue Service (the “Service”) of the Regulations and the Code, (d) existing judicial decisions, (e) such other authorities as we have considered relevant, and (f) our interpretation of the foregoing authorities, all of which such preceding authorities are subject to change or modification at any time (possibly with retroactive effect).

Based solely upon the foregoing, and subject to the assumptions, qualifications and limitations stated herein and the assumptions, qualifications and limitations set forth in the S-3 Registration Statement, we are of the opinion that the discussions set forth in the S-3 Registration Statement under the subheading “Material United States Federal Income and Estate Tax Considerations” to the extent that such discussions relate to matters of United States federal income and estate tax law, are accurate in all material respects.

We express our opinion herein only to those matters specifically set forth above and no opinion should be inferred as to the tax consequences, whether federal, state, local or foreign, of any transactions related to the S-3 Registration Statement, or contemplated by the S-3 Registration Statement. We do not express any opinion herein concerning any law other than the federal income tax law of the United States. No assurance can be given that our opinion will not be challenged by the Service or any other taxing authority, or that any such challenge will not be successful.

The foregoing opinion reflects our best professional judgment as to the correct U.S. federal tax consequences of the transaction to which this opinion relates. Our opinion is expressly conditioned on, among other things, the accuracy of all such facts, information, statements and representations as of the date hereof. Any material change in the law, authorities, or facts referred to, set forth, relied upon or assumed herein, or in the S-3 Registration Statement could affect the conclusions stated herein. This opinion is expressed as of the date hereof, and we are under no obligation to supplement or revise our opinion to reflect any changes (including changes that have retroactive effect) (a) in applicable law or (b) that would cause any statement, representation or assumption herein to no longer be true or correct.

Sigma-Aldrich Corporation

October 25, 2010

Page 3

This opinion has been prepared for Sigma-Aldrich in connection with certain transactions set forth in the S-3 Registration Statement. We hereby consent to the filing of this opinion as Exhibit 8.1 to the S-3 Registration Statement, and to the references to our firm name therein. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations thereunder.