You don't want them to have access to anything moldy. There is also a wide variety of Chinchilla Treats on the market today. I have found that my chin likes a little of them all. Caution - Do not feed too many treats. Hay needs to have had proper circulation while being stored as well.
Molds can be a problem with too dry of hay.
Always check your hay to make sure that is not molding. Sometimes smelling of the hay will let you know if it has molded. Le gume Hays such as Alfalfa could be stored for up to 9 months. However, most reputable breeders will tell you to use your feeds within 90 days. Hays such as Timothy Hay are good as long as they remain insect free, rodent free, and free of molds and weeds.