Totally depends. I would start by checking your chain with a tool and seeing how worn it is, and inspecting your cassette as well. If either one is fried, there you go. Otherwise, have a look at how the chain sits on the chainring. Especially on a big 52 or whatever, you can really see if it's worn and the pins don't want to sit in the center of the notches between the teeth.
'''96 Litespeed Catalyst, '05 Litespeed Firenze, '06 Litespeed Tuscany, '12 Surly Pacer, All are 3x8,9 or 10. It is hilly around here!
Chainrings, unless very badly worn and the teeth are obviously hooked, are pretty tolerant of chain condition. I've put brand new chains on chainring sets with 25,000+ miles on them and they run and shift just fine. Casettes are another matter altogether.