"Chock-a-block is actually a fairly widely known North American term, I'm told. I know it well and would use it, though there's a faint air of being slightly out of date about it. In Britain, it's now common to hear the abbreviated forms chocka (or chocker), which are both from World War Two services' slang, and in Australia the closely related chockers.
Chock here is the same word as in chock-full, jam-packed full or filled to overflowing. One meaning of chock in the nineteenth century was of two things pressed so tightly against each other that they can't move. This led to the nautical term that's the direct origin of the phrase. Block refers to the pulley blocks of the tackle used for various hauling jobs on board ship. These worked in pairs, with the ropes threaded between them. When the men hauling tackle ropes had hoisted the load as far as it would go, the two pulley blocks touched and could move no further. They were then said to be chock-a-block, or crammed together.
The origin of chock is complicated and not altogether understood. It's clear that there has been some cross-fertilisation between it and chock in the sense of a lump of wood used as a wedge to stop something moving. That's closely enough related to our sense to make it seem as though it might be the same word. But the experts think that chock in chock-a-block actually came from chock-full.
That has been around at least since 1400. It comes from a different source, the verb chokken, as in the Middle English phrase chokken togeder, crammed together. This in turn may be from an Old French verb choquier, to collide or thrust. One of the problems of working out the origin has been that chock-full has appeared in several different spellings — including chuck-full and choke-full — reflecting users' uncertainty about where it comes from."
Courtesy of 'World Wide Words'
http://www.worldwidewords.org/qa/qa-cho3.htm
