Yes, chinchillas love to eat the branches of a Willow Tree.
It is perfectly safe for a chinchilla to chew on and eat these tree branches. The wood on this tree is very slender and very tough.
The leaves on this type of tree are mostly elongated but some are also oval in shape.
The reason chins love to chew on this tree is that they find it easy to chew on.
However it is important to note that you will need to make sure the treat is not coated with any pesticides or anything else that would harm you chin before letting them chew on the branches.