My use of "jump" means that the chain rides up the teeth in the chainring or cog until it drops down into the next valley behind that tooth. On my bike, it usually stays on the same chainring or cog while it's doing that. Looking down at it when it's under heavy load, it looks like the chainring suddenly gets larger as the chain bushings all slide over the top of the tooth that was driving them. If you look at the chainring very closely, and it's the chainring that's the problem, you'll see that the valleys between the teeth are asymmetrical - one side is nice and rounded and the other looks kind of hooked. Look at your cassette, too, and see what the teeth look like there. Are the teeth on every cog about the same shape, or are there one or two cogs that have differently shaped teeth, perhaps because they are your favorite gears?

Yes, it's entirely possible to wear out a cog or chainring in 3000 miles. Moreso if you ride in the rain. Moreso if you haven't been religious about keeping your chain clean and oiled. Clean and lube your chain every time it looks dirty to you. Grab the chain between your fingers and twist it. Does it have a gritty sound? Needs maintenance. Well maintained chains last longer, and make the rest of the drivetrain last longer, too. I use one of those boxes that you put solvent into, hook onto the rear der and the chain passes through it. Works well and it's quick. Then dry it very carefully. I use a heat gun with a shrinktube attachment. Then try Finish Line Ceramic lube. Use the heat gun to warm that into the chain, too. You do that once a week and your chain will last a long time.

Oh - and buy a Park chain checker and use it once/week after oiling. Change the chain when it's well into the red.