An interjection shouted out after a person experiences an excrutiatingly painful burn, or insult. The "Ch-ch" noise refers to the sound of the cocking of a shotgun. The "burn!" replaces the sound of "bang!". That's how painful this particular burn must have been.
Boy: I don't know why you wear a bra. It's not like you have anything to fill it.
Girl: And yet you still wear pants.
Random friend: Ch-Ch-BURN!!!