Originally Posted by FBinNY

Actually a slightly worn sprocket that's causing skipping with a new chain needs very little break in time to wear off the corners of the teeth that are the issue and run fine. If he skipping is sporatic enough that the rider can live with it, it'll get better. The problem is that the skipping is usually worse than people will tolerate even for an hour.

There's also a technique for manually fixing a problem sprocket, using a Dremel to grind a bit off the back top corner of each tooth on the problem sprocket. This is useful for an otherwise OK cassette that skips on one sprocket.