SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

Report of Foreign Private Issuer
Pursuant to Rule 13a-16 or 15d-16 of the

Securities Exchange Act of 1934

For the month of April 2014

Commission File Number 1-13758

PORTUGAL TELECOM, SGPS, S.A.

(Exact name of registrant as specified in its charter)

Av. Fontes Pereira de Melo, 40
1069 - 300 Lisboa, Portugal

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F.

Form 20-F x  Form 40-F o

 Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes o  No x

Announcement  |  Lisbon  |  3 April 2014

Maximum number of shares to be issued in Oi’s offer

Portugal Telecom, SGPS S.A. (“PT”) hereby informs on the material fact disclosed by Oi, S.A. (“Oi”) on the maximum number of shares that may be issued in the primary offering of shares of Oi, according to the company’s announcement attached hereto.

www.telecom.pt

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Oi S.A.

Corporate Taxpayers’ Registry (CNPJ/MF) No. 76.535.764/0001-43

Board of Trade (NIRE) No. 33.30029520-8

Publicly-Held Company

MATERIAL FACT

Oi S.A. (“Oi” or the “Company”, BM&FBOVESPA: OIBR3, OIBR4; NYSE: OIBR and OIBR.C) in accordance with article 157, paragraph 4 of Law No. 6,404/76, pursuant to CVM Instruction No. 358/02 and in furtherance of the Material Facts released on October 2, 2013 and February 20, 2014, notifies its shareholders and the market in general that, in a meeting held on April 1, 2014, the Board of Directors of the Company approved, among other things, the maximum number of shares that may be issued in the primary offering of common and preferred shares of Oi, whose request for registration is being analyzed by the CVM (the “Offering”).

In connection with the Offering, Oi may initially offer 1,917,028,657 common shares and 3,834,057,315 preferred shares, totaling 5,751,085,972 shares, including shares in the form of American Depositary Shares, represented by American Depositary Receipts.  The number of shares initially offered, not considering the exercise of the Hot Issue (defined below), may be increased, at the option of the lead coordinator, by up to 15%, in other words, by up to 287,554,298 common shares and 575,108,597 preferred shares, totaling 862,662,895 shares, in order to fulfill subsequent demand for the Offering (the “Over-Allotment Option”). Finally, the number of shares initially offered, not considering the exercise of the Over-Allotment Option, may be increased, at the Company’s discretion, in agreement with the global coordinators of the Offering and the other international underwriters, by up to 20%, in other words, by up to 383,405,731 common shares and 766,811,463 preferred shares, totaling 1,150,217,194 shares (the “Hot Issue”).

Oi will maintain its shareholders and the market informed of any subsequent events related to the Offering.

Rio de Janeiro, April 2, 2014.

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Oi S.A.

Bayard De Paoli Gontijo

Chief Financial Officer and Investor Relations Officer

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Additional Information and Where to Find It:

Oi S.A. (“Oi”) has filed a registration statement (including a prospectus) with the U.S. Securities and Exchange Commission (the “SEC”) for the offering to which this communication relates. Before you invest, you should read the prospectus in that registration statement and other documents Oi has filed with the SEC for more complete information about Oi and this offering. You may get these documents for free by visiting EDGAR on the SEC’s website at www.sec.gov. Alternatively, Oi will arrange to send you the prospectus after filing if you request it by calling toll-free 1-855-672-2332.

Special Note Regarding Forward-Looking Statements:

This communication contains certain forward-looking statements. Statements that are not historical facts, including statements about our beliefs and expectations, business strategies, future synergies and cost savings, future costs and future liquidity are forward-looking statements. The words “will,” “may,” “should,” “could,” “anticipates,” “intends,” “believes,” “estimates,” “expects,” “plans,” “targets,” “goal” and similar expressions, as they relate to Oi, are intended to identify forward-looking statements and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, tendencies or expected results will actually occur. Such statements reflect the current views of management of Oi and are subject to a number of risks and uncertainties. These statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, corporate approvals, operational factors and other factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations. All forward-looking statements attributable to us, or persons acting on our behalf, are expressly qualified in their entirety by the cautionary statements set forth in this paragraph. Undue reliance should not be placed on such statements. Forward-looking statements speak only as of the date they are made. Except as required under the U.S. federal securities laws and the rules and regulations of the SEC or of regulatory authorities in other applicable jurisdictions, we do not have any intention or obligation to update or to publicly announce the results of any revisions to any of the forward-looking statements to reflect actual results, future events or developments, changes in assumptions or changes in other factors affecting the forward-looking statements. You are advised, however, to consult any further disclosures Oi makes on related subjects in reports and communications Oi files with the SEC.

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SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: April 3, 2014

FORWARD-LOOKING STATEMENTS

This document may contain forward-looking statements. These statements are statements that are not historical facts, and are based on management’s current view and estimates of future economic circumstances, industry conditions, company performance and financial results. The words “anticipates”, “believes”, “estimates”, “expects”, “plans” and similar expressions, as they relate to the company, are intended to identify forward-looking statements. Statements regarding the declaration or payment of dividends, the implementation of principal operating and financing strategies and capital expenditure plans, the direction of future operations and the factors or trends affecting financial condition, liquidity or results of operations are examples of forward-looking statements. Such statements reflect the current views of management and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, trends or results will actually occur. The statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, and operating factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations.

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