Green’s Dictionary of Slang

(US) an illicit drinking establishment; also attrib.

c.1926		in P. Smith Letter from My Father (1978) 169: After a drink with them all at a ‘speak’ around the corner.
1929		W. Winchell On Broadway 14 Oct. [synd. col.] Broadway visitors eat more delicacies, sweets, and drink ‘speak’ stuff.
1936		A. Seale N.Y. Age 1 Aug. 7/4: Mike’s Moulin Rouge [...] was the ace ‘speak’ of Harlem.
1940		S. Lister Mistral Hotel (1951) 75: Last time I saw you you was shakin’ ’em at Clancy’s speak on 52nd.
1952		Lait & Mortimer USA Confidential 231: If they want to drink after hours, many all-night speaks run in the lower East Side.
1967		(con. 1932) S. Harris Hellhole 38: Sam Schwartz’s Speak, which catered to homosexuals.
1970		(con. 1920s) ‘Red’ Rudensky Gonif 94: St. Louis was booming [...] but the Feds had an uncommonly adept knack of knocking over speaks.
1993		(con. 1920s) I.L. Allen City in Sl. (1995) 72: Most people called them speakeasies. The term was soon shortened to speak.