Fur chewing can be for various of reasons, and can even become habit if the reason isn't solved quickly enough, like a person chewing their nails. The most common reasons are stress, boredom, pain, and genetic predisposition to fur chewing. Fur chewing, also called barbering, is not detrimental on it's own, so long as it's just fur not chewing creating sores. Also it's not that common but if they are swallowing the hair they can get a hairball that causes a gut blockage (they can't throw up), so something to watch for.
For the issues of stress and boredom they can generally be fixed by a change in environment to one that is more relaxed and offering more toys as well as more out of cage time and interaction. If it's caused by pain getting that sorted could help stop the chewing, generally with pain the continue chewing causing sores because they are trying to get rid of it. If it's become a habit or the chin is just generically a fur chewer you might have luck reducing it with distractions (toys, playtime, etc), but most will resort to it if things aren't perfect.
Yes, I would. Eye appeal is, of coursed, important, but it's more important that a chinchilla has a safe and happy home. I don't necessarily agree that fur chewing can be "cured" though as it can be genetic as well as environmental. And, as with any bad habit, once you start it's hard to stop.