Yeah, my chins are in and out when it comes to nibbling. I have a black velvet male who LOVES eating clothes and seems willing to nibble on skin (not even just nails or fingers, but smooth skin such as on a forearm), but he's special in that sense haha.
One biting story about him though - he started fighting with his cage mate almost a year back, so we had to separate them completely. A few months back, the black velvet darted from my grasp and got into the other male's cage section, and upon separating them he bit me very hard and aggressively on my finger, thinking I was his nemesis. Needless to say, there was lots of blood and I initially felt like I would need stitches because it was quite deep, but it healed without much fuss. Those who asked what happened were quick to say "oh, well don't you think that maybe owning chinchillas isn't such a great idea?" or "yikes, chinchillas.." and I was even quicker to say - no, it was a mistake on MY part to have allowed them to come into contact again at all. But it IS a lesson for me in general to realize firsthand how deeply and strongly chins can bite, and how truly aggressive they can be towards each other when they feel threatened. Thankfully no chins were hurt!
But with my other 4 chins, they are very sweet and have never bitten nor nibbled on me or my clothing - my ladies prefer to lick, actually!