c.1400, from Middle English chokkeful, possibly from choke (see cheek (n.)), equivalent to cheek + full. Or it may be from Old French choquier “collide, crash, hit” [similar to shock].
Middle English chokkeful already had the same meaning as modern chock-full. Both this word and choke “to strangle” likely derive ultimately from Old English words meaning “jaw, cheek.” The end result is the same: a mouthful.
Alternately, chokkeful may derive from a more violent word: forced full.
(Some offer a false etymology based on the kind of chocks used in carpentry and shipbuilding: full up to the chocks, perhaps. However that sense of chock only dates to the 1670s, far too late to influence the Middle English word. However, the form chock-a-block full is indeed due to association with that word, chock.)
Modern English dictionary
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