Post some pictures of the bike, the chainrings, and the rear cassette. Chances are, what you are seeing on the chainrings is normal and part of the design. The teeth on the rings are trimmed in certain areas to aid with shifting. Chainrings are not a common wear item so unless you have lots of miles on the bike and have never replaced your chain, the rings themselves are not likely the problem.

As for the actual cause of the jumping, what exactly is the chain doing? Is it falling off the chainrings?