Chinchillas, in general, do not need to have their nails clipped. When I hold my chinchillas, I can sometimes feel their nails on my skin but they aren't long enough to be clipped. Can you actually see the length of the nails on their back paws? Is the nail catching on anything? If it is visibly long, you can use animal clippers to cut the nail but please be careful when you clip the nail, you don't want to cut the "quick" of the nail. The quick of the nail is where the vein lies in the nail bed. If you don't feel comfortable doing this or your chinnie isn't fond of being handled, you may want to take him/her to the vet to get it professionally done.