Have you tried contacting the Chelsea Clock Company, which is still very much in existence? See chelseaclock.com.
This page suggests that, for a price, Chelsea Clock will provide a certificate of origin for a given Chelsea clock, including its date of manufacture and to whom it was sold. See http://www.chelseaclock.com/Certificates-Of-Origin.
But my guess is that the records of Chelsea Clock will show, in your case, that the clock was sold as part of a large lot to a given shipyard or (in a much larger lot) to the U.S. Maritime Commission, which contracted for the construction of ships during World War II, or some other related agency. The clock would not have been "sold" to an individual ship but rather to the government or to a shipyard.
But knowing the date of manufacture and, possibly, the name of a shipyard, would at least narrow things down. This web page, for example, lists World War II shipyards building various kinds of vessels, particularly Liberty and Victory ships, tankers, other cargo vessels and small naval vessels: http://shipbuildinghistory.com/history/shipyards/4emergencylarge.htm. Links to individual shipyards will list names of ships, type, and dates of launch. (There were hundreds if not thousands of ships other than Liberty ships in which your clock could have been installed.)
You might also contact the U.S. Archives and Records Administration to see if they might have shipyard records or U.S. Maritime Commission records that might point to the installation of this clock. I would try the Modern Military Records Unit at this address:
National Archives and Records Administration
Modern Military Records (NWCTM)
8601 Adelphi Road
College Park, MD 20740-6001
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website