The Rye Grass is high in nutrition. The grass is a feed for animals like cow and sheep. Yes, chinchillas can also eat Rye Grass. It is good for your chins. However, make sure that the grass feeded to your chins is to be dry. As chins have a sensitive digestive system, the fresh Rye grass may affect the stomach of the chinchillas. So avoid feeding your chinchillas more fresh Rye grasses.