If it's acrylic paint, you might just want to try some water and a q-tip? it might do the trick. You could also try alcohol, but you'd have to be very cautious because it will eventually 'dull' the chrome and melt it away too.
If you're talking about a part that's been completely painted, then you're probably better off to strip the whole thing and re-chrome it using Alclad II.
If you're talking about some small 'slips' where you got a little paint on the chrome, then try using a piece of balsa wood or a toothpick to 'scrape' the dried paint off of the chrome. If you're cautious, you can do it without damaging the chrome underneith.
Good luck
Murray