I have a chain stutter on one of my gears. How do a fix this?
It's also more noticeable on hills.
By stutter, do you mean skipping? Or is it just noise?
Noise - Probably r. derailleur adjustment
Popping into different gear - Probably r. derailleur adjustment
Skipping (Chain pops over the cassette cogs when under pressure) - Worn chain
Check your rear derailleur adjustment, but it sounds more like a worn chain. If you replace the chain early, the cassette should last a bunch of chains, and the chainrings should last a bunch of cassettes. Since it is skipping, more than likely the cassette will be toast too.
You can check chain stretch with a ruler (google it), cassette and chainrings are trickier, generally they should not look saw-toothed. Chainrings usually last a long time, so they are probably fine unless you ride a whole lot, or your bike is older.
Your best bet is probably to go to a bike shop. That is unless you want to get the tools and learn how to do it yourself. It's not very difficult, but if you don't ride a lot, might not be worth the expense.