What stomach chamber doesn't work at birth for a calf?

The reticulum and rumen (and likely omasum) of a calf are underdeveloped at birth and do not reach full maturity until the calf is around 3 months of age, after the calf has began to eat grasses and/or grains like its mother. Calves will start eating the same things as their mother when they're only a week or two old. So that's not to say that there's particular compartments that do not work at birth, since all compartments are functional, it's just that they're not nearly as functional as that of an adult bovine. A calf makes the action of chewing cud at a few weeks of age, but is not actually chewing cud, since the rumen is not functional enough to enable rumenation.

Young calves have a special tube-like structure called the oesophageal (or esophageal) groove which directs milk straight from the oesophagus to the abomasum. This is the final (fourth) stomach chamber of the calf. This means that milk bypasses the reticulum, rumen, and omasum (to a lesser extent). The oesphageal tube begins to disappear when the reticulo-rumen nearly reaches maturation, and when the calf becomes less dependent on milk and more on forages. The groove pretty much disappears by the time the calf reaches a point where it is no longer considered a calf, which would be at yearling stage.