I don't think so, mine never did, although they do shed a lot of hair, the reason being that they have 20 hairs coming out of each hair follicle. All other animals have 2. Thats why chinchilla fur coats were so popular - lovely snuggly warm! A shame so many little peeps have to snuff it for a jacket tho. In the world of genetics you think they could grow fur without involving animals!?! Nice idea but maybe not.