Chins often chew due to boredom/lack of environmental stimuli, or stress, and there is a genetic predisposition for this behavior. Sometimes just being in a new environment (new home, new cage, etc.) can cause a chin to chew... or sometimes just because they are bored or have nothing else to chew on, they'll begin to chew on themselves. I think of fur-chewing like feather-plucking in birds... it is done when they are stressed or are not being stimulated - in birds, it is important for them to have toys to play with, things to destroy and shred, puzzle toys to figure out, etc, where they can take out their frustrations on or give their attention to rather than themselves.
Think of ways to stimulate Furby such as hiding a treat in a pile of hay, stuffing hay into a tube, hiding apple sticks in various places in his cage, giving him different types of toys to play with/chew on - things that will keep him occupied. Chins are very curious and having new things to nibble on and explore often helps with chewers.
Sometimes fur-chewers just can't break the habit... and occasionally, will fur-chew cagemates as well.
