No, chinchillas cannot eat sesame seeds at all.
The reason being is that sesame seeds are rich in fat, calcium and phosphorus content. These nutritional elements are really bad for chinchillas.
There is a chance if your chinchilla was to eat sesame seeds that it would cause some harm to their body.
One of the common side effects would be diarrhea. Another possible negative health effect would be skin rashes and hair loss.
So do not feed sesame seeds to your chinchilla as they are bad for their health.