Exhibit 5.1

December 5, 2011

318008 | Legal Opinion TO | equity - to legal opinion draft 120511.docx

Transocean Ltd.

Ladies and Gentlemen:

We have acted as special Swiss counsel to Transocean Ltd., a Swiss corporation (the Company), in connection with the Registration Statement on Form S-3 (Registration No. 333-169401) (the Registration Statement) filed with the Securities and Exchange Commission (the Commission) under the Securities Act of 1933, as amended (the Act), a related prospectus, dated September 16, 2010, and prospectus supplement (the Prospectus Supplement), dated November 29, 2011 (together, the Prospectus), with respect to the issuance, offer and sale (the Offering) of 29,900,000 registered shares of the Company with a par value of CHF 15 each (the New Shares).

As such counsel, we have been requested to render an opinion in connection with certain matters of Swiss law.

Capitalized terms used but not defined herein shall have the meanings assigned to such terms in the Documents (as defined below) unless otherwise defined herein.

I.          Basis of Opinion

This opinion is confined to and given on the basis of the laws of Switzerland in force at the date hereof. Such laws and the interpretation thereof are subject to change. In the absence of explicit statutory law, we base our opinion solely on our independent professional judgment. This opinion is also confined to the matters stated herein and is not to be read as extending, by implication or otherwise, to any other agreement or document referred to in any of the Documents (as defined below) or any other matter.

For purposes of giving this opinion, we have only examined originals or copies of the following documents (collectively the Documents):

(i)         a copy of the public deed of incorporation (Gründungsurkunde) of the Company, dated as of August 14, 2008;

(ii)        a legalized copy of the articles of association of the Company, dated December 4, 2011, in the form filed with the Commercial Register of the Canton of Zug, Switzerland, on December 5, 2011 (the Articles);

(iii)       an excerpt from the journal (Tagebuchauszug) of the Commercial Register of the Canton of Zug, dated December 5, 2011, relating to the Company (the Excerpt);

(iv)       an electronic copy of the organizational regulations (Organisationsreglement) of the Company, dated as of October 8, 2008 (the Organizational Regulations);

(v)        an electronic copy of the register of uncertificated securities (Wertrechtebuch) of the Company, dated as of December 5, 2011, confirming the creation of, in the aggregate, 29,900,000 new uncertificated securities (Wertrechte) of the Company (the Uncertificated Securities Register);

(vi)       an electronic copy of the Registration Statement and the Prospectus; and

(vii)      an electronic copy of (i) an excerpt from the minutes of a meeting of the Board of Directors of the Company dated May 13, 2011, (ii) the minutes of the resolutions of the board of directors of the Company, dated November 18, 2011, regarding, among other things, the authorization of the Offering and the actions to be taken in connection therewith, (iii) the minutes of the resolutions of the board of directors of the Company, dated November 18, 2011, regarding the capital increase based on the authorized share capital (Durchführungsbeschluss), (iv) the public deeds on the resolutions of the board of directors of the Company, dated November 29, 2011, and December 4, 2011, respectively, regarding the ascertainments regarding the authorized share capital increases (Feststellungsbeschluss), and (v) the minutes of the resolutions of the special committee of the board of directors of the Company, dated November 29, 2011, regarding, among other things, the launch of the Offering, the aggregate number of New Shares, and the general terms and conditions of the Offering (collectively the Resolutions).

No documents have been reviewed by us in connection with this opinion other than the Documents. Accordingly, we shall limit our opinion to the Documents and their legal implications under Swiss law.

In this opinion, Swiss legal concepts are expressed in English terms and not in their original language. These concepts may not be identical to the concepts described by the same English terms as they exist under the laws of other jurisdictions. With respect to Documents governed by laws other than the laws of Switzerland, for purposes of this opinion we have relied on the plain meaning of the words and expressions contained therein without regard to any import they may have under the relevant governing law.

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II.         Assumptions

In rendering the opinion below, we have assumed the following:

(a)        all documents produced to us as originals are authentic and complete, and all documents produced to us as copies (including, without limitation, fax and electronic copies) conform to the original;

(b)        all documents produced to us as originals and the originals of all documents produced to us as copies were effectively executed and certified, as applicable, in the manner and by the individuals appearing on such documents;

(c)        except as expressly opined upon herein, all information contained in the Documents is, and all material statements given in connection with the Documents are, true and accurate;

(d)        no laws other than those of Switzerland affect any of the conclusions stated in this opinion;

(e)        all authorizations, approvals, consents, licenses, exemptions and other requirements, other than those required under Swiss law, for the offering, issuance and sale of the New Shares, for the filing of the Registration Statement and the Prospectus, for the distribution of the Prospectus, or for any other activities carried out in view of, or in connection with, the performance of the obligations expressed to be undertaken by the Company in the Prospectus and the Offering, have been duly obtained and are and will remain in full force and effect, and any related conditions to which the parties thereto are subject have been satisfied;

(f)         the Excerpt is correct, complete and up-to-date, and the Articles, the Organizational Regulations and the Uncertificated Securities Register are in full force and effect and have not been amended, and no shares of the Company have been issued based on the conditional share capital of the Company, other than as reflected in the number of shares as set forth in the Articles and the Excerpt; and

(g)        the Resolutions (i) have been duly resolved in meetings duly convened and otherwise in the manner set forth therein, (ii) have not been rescinded or amended, and (iii) are in full force and effect.

III.        Opinion

Based on the foregoing and subject to the qualifications set out below, we are of the opinion as of the date hereof:

1.          The Company has been duly incorporated and is validly existing as a corporation (Aktiengesellschaft) under the laws of Switzerland with all requisite corporate power and authority to enter into, to perform and to conduct its business as described in the Articles.

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2.          The Company’s share capital registered in the Commercial Register of the Canton of Zug, as evidenced in the Excerpt, amounts to CHF 5,477,029,470, divided into 365,135,298 registered shares with a par value of CHF 15 each. The New Shares have been validly issued, fully paid and are non-assessable.

IV.       Qualifications

The above opinion is subject to the following qualifications:

(a)        The lawyers of our firm are members of the Zurich bar and do not hold themselves out to be experts in any laws other than the laws of Switzerland. Accordingly, we are opining herein as to Swiss law only and we express no opinion with respect to the applicability thereto, or the effect thereon, of the laws of any other jurisdiction.

(b)        We express no opinion as regards the withdrawal of shareholders’ preemptive rights (Bezugsrechte) in connection with the Offering.

(c)        We express no opinion as to any commercial, financial, accounting, tax, calculating, auditing or other non-legal matter.

(d)        We have not investigated or verified the truth or accuracy of the information contained in the Prospectus, nor have we been responsible for ensuring that no material information has been omitted from it.

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We have rendered this opinion as of the date hereof and we assume no obligation to advise you on changes relevant to this opinion that may thereafter be brought to our attention.

We hereby consent to the filing of this opinion as an exhibit to the Current Report on Form 8-K and to the reference to us under the heading “Legal Matters” in the Prospectus Supplement.  In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required pursuant to Section 7 of the Act.

This opinion is furnished by us, as special Swiss counsel to the Company, in connection with the Offering.

This opinion shall be governed by and construed in accordance with the laws of Switzerland.

Sincerely yours,

/s/ Homburger AG

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