Exhibit 99.1

PILGRIM BANCSHARES, INC. COMPLETES STOCK OFFERING

Cohasset, Massachusetts, October 10, 2014 – Pilgrim Bancshares, Inc. (the “Company”), a Maryland corporation and the holding company for Pilgrim Bank (the “Bank”), announced today the completion of the Company’s stock offering and the mutual-to-stock conversion of Conahasset Bancshares, MHC (the “MHC”). Shares of Pilgrim Bancshares, Inc. common stock will begin trading on Monday, October 13, 2014, on the OTC Pink Marketplace under the symbol “PLRM.”

The Company sold 2,182,125 shares of common stock, representing the adjusted maximum of the offering range, at $10.00 per share, for gross offering proceeds of $21,821,250, including the sale of 179,807 shares to the employee stock ownership plan in the stock offering. Additionally, 65,464 shares of Company common stock and $70,360 in cash have been contributed to the Pilgrim Bank Foundation in connection with the conversion and offering.

As previously announced, the stock offering was oversubscribed in the first category of the subscription offering by eligible account holders as of December 31, 2012. Accordingly, eligible account holders will have valid orders filled in accordance with the allocation procedures described in the prospectus and as set forth in the MHC’s Plan of Conversion. “We appreciate the support that we have received from our depositors during this process and welcome our new shareholders,” stated Frank Campbell, President and Chief Executive Officer of Pilgrim Bancshares, Inc.

If you are a first category subscriber and would like to confirm your allocation, you may contact the stock information center at (877) 892-9472 (toll free) from 10:00 a.m. until 4:00 p.m., Eastern Time, Monday through Friday. This information is also available online at https://allocations.kbw.com/.

Keefe, Bruyette & Woods, Inc., A Stifel Company acted as selling agent in the subscription offering, and served as financial advisor to the Company and the Bank in connection with the conversion. Luse Gorman Pomerenk & Schick, P.C. served as legal counsel to the Company and the Bank. Hogan Lovells US LLP served as legal counsel to the selling agent.

ABOUT PILGRIM BANCSHARES, INC.

Pilgrim Bancshares, Inc., the holding company for Pilgrim Bank, had assets of $166.3 million at June 30, 2014. Pilgrim Bank operates as a full service community bank with its main office in Cohasset, Massachusetts, and two additional branch offices in Cohasset and Marion, Massachusetts. Pilgrim Bank provides consumer and commercial deposit and loan products to the South Shore and South Coast areas of Massachusetts, including portions of Plymouth, Norfolk and Bristol Counties. Pilgrim Bank offers residential and non-owner occupied construction, commercial and industrial, and commercial real estate loans in addition to and commercial deposit accounts. Pilgrim Bank also serves consumers through a full suite of consumer banking products including checking accounts, mortgage loans, equity lines of credit and traditional NOW, savings and certificate of deposit accounts. Previously known as Pilgrim Co-operative Bank, Pilgrim Bank has been serving area residents since 1916. For more information about Pilgrim Bank, visit our web site at www.bankpilgrim.com.

CAUTIONARY NOTE REGARDING FORWARD-LOOKING STATEMENTS

This press release, as well as other written communications made from time to time by the Company and its subsidiaries and oral communications made from time to time by authorized officers of the Company, may contain statements relating to the future results of the Company (including certain projections and business trends) that are considered “forward-looking statements” as defined in the Private Securities Litigation Reform Act of 1995 (the PSLRA). Such forward-looking statements may be identified by the use of such words as “believe,” “expect,” “anticipate,” “should,” “planned,” “estimated,” “intend” and “potential.” For these statements, the Company claims the protection of the safe harbor for forward-looking statements contained in the PSLRA. The Company cautions you that a number of important factors could cause actual results to differ materially from those currently anticipated in any forward-looking statement. For information on some of the risks and important factors that could affect the Company’s future results and financial condition, see “Risk Factors” in the Company’s prospectus dated August 11, 2014, as filed with the Securities and Exchange Commission on August 20, 2014.

Contact:

Pilgrim Bancshares, Inc.

Francis E. Campbell, 781-383-0541

President and Chief Executive Officer

fcampbell@bankpilgrim.com