Crammed so tightly together as to prevent movement.
This term is old and has a nautical origin.
The derivation of chock isn't entirely clear but the word is thought to have come from chock-full (or choke-full), meaning 'full to choking'. This dates back to the 15th century and is cited in Morte Arthur, circa 1400:
"Charottez chokkefulle charegyde with golde."
This meaning was later used to give a name to the wedges of wood which are used to secure moving objects - chocks. These chocks were used on ships and are referred to in William Falconer's, An universal dictionary of the marine, 1769:
"Chock, a sort of wedge used to confine a cask or other weighty body..when the ship is in motion."
This is where seafaring enters into the story. A block and tackle is a pulley system used on sailing ships to hoist the rigging. It might be expected that 'chock-a-block' is the result of wedging a block fixed with a chock. That doesn't appear to be the case. The phrase describes what occurs the system is raised to its fullest extent - when there is no more rope free and the blocks jam tightly together. Frederick Chamier's novel The Life of a Sailor, 1832 includes this figurative use of the term:
"Here my lads is another messmate..." - What, another!" roared a ruddy-faced midshipman of about eighteen. "He must stow himself away, for we are chock-a-block here."
We might expect to find a reference to it in relation to ship's equipment before any figurative use, but the earliest I've found is in Richard H. Dana Jr's Two years before the mast, 1840:
"Hauling the reef-tackles chock-a-block."
Chock-a-block also spawned an abbreviated version in the 20th century - chocka (or chocker). This is WWII UK military slang meaning 'fed-up or disgruntled' - as defined in Hunt and Pringles' Service Slang, 1943:
"Chocker, this is the sailor's way of saying he is fed up or browned off."