Can chinchillas eat acorns

I know fruit bearing chestnut trees are far and few anymore, but we do happen to have one that produces so many chestnuts that 3 families run out of ideas on how to use. I was curious if I could give my Chinchilla a chestnut treat maybe every other week. I know the chestnut wood is not good for them, but what about the chestnut itself, which isn't a very sugary nut?