Green’s Dictionary of Slang

1. (US) a burlesque show.

1915		G. Bronson-Howard God’s Man 376: Come off with that small-time humor. It even gets the hook in burlycue.
1927		K. Nicholson Barker III i: At least in burley-Q you ain’t wadin’ knee-deep in soup all the time.
1931		B. Sobel [title] Burleycue: An Underground History of Burlesque Days.
1933		C.G. Booth ‘Stag Party’ in Penzler Pulp Fiction (2006) 93: The Gaiety Theatre [...] had gone burleycue.
1942		W. Winchell On Broadway 28 June [synd. col.] It is burleycue with a cover charge.
1949		F. Brown Dead Ringer 48: Pony in a burlycue.
1952		Lait & Mortimer USA Confidential 94: The Old Howard theatre is the most famous burleycue on the continent.
1974		(con. 1940s) E. Thompson Tattoo (1977) 127: Hey! There’s a real burly-que here!
1992		G. Wolff ‘At the Fair’ in A Day at the Beach (1992) 103: I entered the tent [...] smirking, recollecting burly-que I had seen as a teenager in Florida.
1997		‘Jimmy Vargas & the Black Dahlias’ 🌐 He makes a successful foray mining the nostalgia of his own past life, with his buying and opening of a dancehall cabaret called the ‘BROADWAY.... SWANGO 47’, in San Francisco’s own Burleycue Sin Alley strip of North Beach.
2001		Dance Hist. Archives 🌐 American stage burlesque (from 1865), often referred to as ‘burleycue’ or ‘leg show,’ began as a variety show, characterized by vulgar dialogue and broad comedy, and uninhibited behavior by performers and audience.

2. attrib. use of sense 1; thus burleycue house, a burlesque theater.

1956		‘Ed Lacy’ Men from the Boys (1967) 27: Whenever she worked one of the burleycue houses in New Jersey, I’d go over to watch her.
a.1958		C. Kornbluth [limerick] A burlycue dancer, a pip / Named Virginia could peel in a zip.