I think dried rose hips, dried or fresh papaya, and a nibble or two of a fresh banana are among the best ... each has extra vitamins that are good for a chinchilla and are low in sugar content.
Cranraisins, oyster crackers, Cheerios, dried macaroni shells, mini wheats (plain) and wheat toast are a few others. When adding a new treat, it is best to give your little one that one new treat for a week to make sure he/she is not going to have an allergic reaction or diarrhea from it. Keep a list of those treats he likes and reacts to well and a list of 'no-no' treats that do not set well with him/her.
Chinchillas have allergies the same as humans do ... not all chins can have the same treats.
NO-NO treats for all chinchillas are as important as, if not more important than the good treats. Some of the "no-no" treats can kill.
A chinchilla should never be given:
1) Meat or meat byproducts, they are strict vegetarians ... their systems are not made to digest mean or meat byproducts ... it can and usually does kill a chin.
2) Nuts have natural oils that can not be processed properly and can make a chinchilla have a fatty liver. A fatty liver can kill a chinchilla.
3) Most hard woods do not set well with chinchillas' systems. Remember, chinchillas usually chew and often consume some of their bedding.
4) Cedar puts off a 'fume'/vapor that can cause inflammation in the lungs of a chinchilla.
I'm sure there's lots of others (good and bad) that can be thought of by others.
Jo Ann