For most chins a vet visit causes unnecessary stress if there is nothing wrong, and can create a stress induced issue. Chins don't need shots or deworming, or anything like that so there is little a vet can do for a wellness check. However it's advised to find a chinchilla competent vet as soon as possible (if you haven't already), you need an exotic specialist, but not all know or even will see chinchillas. Most times when a chin needs a vet it needs one right now (and it's in the middle of the night, or the weekend it seems, lol) so it's not a good time to be thumbing through a phone book.
Monitor weight, with a gram scale since they weigh so little, weight loss is normally an early warning that something is wrong, chins are annoyingly good at hiding issues. It's also not uncommon for weight loss to be the only visible symptom of a problem, until it's advanced and too late.