Green’s Dictionary of Slang

in a gulping manner; usu. in the context of downing a drink fast and in a single draught.

c.1936		in R.A. Reuss Field Collection of Songs (1965) 173: So drink chug-a-lug, chug-a-lug [HDAS].
1958		(con. 1950) E. Frankel Band of Brothers 278: So drink, chug-alug-chug-alug / o drink, chug-alug-chug-alug.
1959		M. Richler Apprenticeship of Duddy Kravitz (1964) 169: The football crowd. Well, you know, drink chug-a-lug and all that.