Brewer's: Chuck Full
Probably a corruption of chock full or choke full —i.e. full enough to choke one.
“Ayr was holding some grand market; streets and inn had been chokefull during the sunny hours.” —Carlyle, in Froude's Jane W. Carlyle, vol. i. letter 1xxxvii. p. 275.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894