I agree with others, that more than likely he will be okay. The only thing that chinchillas can sometimes get, from going without water for a length of time, is a bladder or urinary infection.
I once took in a rescue who had gone without water for about a week or so(he was dumped at the SPCA with his other buddies who had all gone without water too.).
He developed a bladder infection, which my vet quickly diagnosed and explained that it happens sometimes when they go without water. Symptoms of the bladder infection were peeing frequently, and for him, he had a milky white discharge after he urinated. A quick round of antibiotics and he was back to his normal self though.