The Online Etymology Dictionary offers more detail:
c.1400, chokkeful “crammed full,” possibly from choke “cheek” (see cheek (n.)). 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.
(Wiktionary offers 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.)