Green’s Dictionary of Slang

1. a female breast.

1929		W. Winchell On Broadway 10 Aug. [synd. col.] A lass [...] in a sport sweater revealing shapely Mae Wests.
1945		E. Wilson I Am Gazing Into My 8-Ball 34: Mae West’s famous Mae Wests are really falsies.
1960		J. Franklyn Dict. of Rhy. Sl.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.
1981		P. Wright Cockney Dialect and Sl. 98: Mae West ‘chest’.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.

2. a vest.

1940

Western Dly Press 13 Aug. 3/5: The R.A.F.'s name 'Mae West' is Cockney rhyming slang for 'vest'.

3. the best (thing).

2002

D. Shaw ‘Dead Beard’ at www.asstr.org 🌐 Yes, that gal is really riding on the tube up her kyhber pass and the mae west is still to come.