Chinchillas will chew their fur because they aren't getting what they need in their diet, not getting enough hay (or any hay at all), or they are in pain...along with the reasons already stated.
I've seen many chins that stop chewing when they are taken off of stale, nutritionally incomplete diets and put onto a decent diet of fresh pellets and hay. Along with the addition of toys and fun things to do do, you may want to look at your chin's diet and see if there's anything that needs changing.
Some chins are just fur chewers and won't stop for any reason. However, most cases of fur chewing have a cause and will stop once the chin is given the right diet or is in the right environment or the cage is kept clean enough, etc.