If your other chin has it too then it's probably ringworm or something like it. You might want to take it to vet to get an specific diagnosis. The chinchilla dust in the air can spread the fungus to the other chins and to you.
Clean your cages and dust bath pans and replace the dust after each dust bath. You will want to sterilize them with a cleaner safe for pets otherwise your pets could be infected again before they are cured with the powder.
Make sure to wash your hands carefully before and after you handle your pets. If you happen to become infected yourself it can take 6 weeks or more to cure it. This can be a long fight.
I had a cat with ringworm before and it was very difficult to cure but that was also because it was in a place where the cat could lick it and cause damage. I also contracted it from the cat which was no fun. Be grateful it's on the nose and try to keep it from spreading to where your chin can reach it. Hope this helps.