Multilevel cages, similar to those designed for ferrets, work well, as long as there are no areas where a chinchilla could get its limbs or feet caught.
Multilevel cages with opportunity to exercise, burrow, eat and drink are appropriate.
Food offered in the form of a reward at the end of a maze or at the top of
a multilevel cage encourages rats to get exercise to obtain their meals and can help limit weight gain in predominantly sedentary rodents.