How old is she? Young ones can be mouthy and not realize they are harming you. Especially when you first start giving them treats. We just withdraw our fingers and say "eh don't bite". By the time they are 4-5months old they usually start to improve and then they start to get a daily treat. They still may nibble a little but they learn the limit to avoid causing pain. My adults can slide their teeth carefully across my fingers until they get ahold of a single piece of oatmeal and pull it loose. My young ones tend to go "treat!" *chomp!* and I have to pull the treat away, tell them not to do that, and try again. Occasionally it takes 4 or 5 tries. I haven't actually had any chinchilla break skin though. Just hard pinches.