Nibbling on, or licking your arm, hand, face, etc is usually a means of "grooming" you ... if he/she is grooming you, then they have accepted you as a big chin ... a very honerable and delightful status in the chinchilla world! They love you
If they nip you firmly, you have done something wrong ... best to figure it out and not do it again.
OR the next step will happen: IF you continue to scare or frighten or hurt them ... they bite you hard enough to hurt, or hard enough to break skin, or bring blood ... you have definitely done something that has upset or frightened them ... find out what it was and avoid doing it again.
Also now if he's in this mood and we put him back in his cage and we stick our fingers in to pet him he sniffs then tries to nibble them.
Suggestions on how to deal with this?
Is he nibbling the finger or the finger nail? They do like to give "manicures" ... but make sure your hands are freshly washed ... if there is a smell of food on them ... he may think it is a treat and decide to take a bite to see if it tastes good.
Jo Ann