Although many chinchillas will be fine having some peanuts, or peanut butter, it is not advised for you to give them to your chinchilla. The reasoning behind this is that nuts, like peanuts are high in fats, and can lead to major health problems down the road.
The First Time:
Some chinchillas can also be allergic to peanuts. If you decide to give some to your pet, make sure you give a very small amount at first, and watch for odd behaviour.