Hi..
I think it is fine for a chinchilla to sleep on its side. I have several that do! I have to admit though that the first time I saw one sleeping on its side it scared me half to death. Now I think that the chinchillas are just very comfortable with their surroundings. They can stretch out and sleep peacefully.
I even have one female that just had kits and she sleeps on her back with her feet up in the air so the kits can nurse while she sleeps.