No, Chinchillas can’t eat roaches. Roaches are type of insect which chinchilla won’t eat. As chinchilla may eat the grass, hay and it’s related items, roaches are not being liked by the chinchilla. Chinchilla like the vegetarian foods only. Sometimes it won’t take non-vegetarian foods. Suppose if chinchilla catch the roaches means there will be a chance that roaches may bite the chinchilla. So chinchilla don’t eat roaches.