3:30 am is highly active playtime for mine. Probably hears something you can't and alarm-calls. Could be lonely if he's an only chin. They like company and if barking gets your attention, they'll sometimes do it for that. But my chins make happy, chirpy, mousy kind of calls to me when they're in...
One of my chinchillas (two lovely ladies approximately 3 1/2 years old) definitely has nightmares. She goes in bouts. She and her cage mate like to sleep in the same hammock together, or on a broad corner ledge. When she has a nightmare, her barking wakes the other chinchilla up, who just moves...