So . . . here are all the causes of chain skip that I've observed in my short life: bent chain, worn chain, chain with stiff link, badly adjusted derailleur, bent derailleur hanger, worn cassette/freewheel cogs, dirt caked between cassette/freewheel cogs, bent cassette freewheel cogs, otherwise damaged cassette/freewheel cogs, and bent chainrings.

Where do you want to start?