We were recommended her by another breeder. We didn't really have a need to see her until our first emergency c-section. It would have been an emergency emergency but she fit us in so we didn't have to take her to an e-vet. She did awesome and both kits survived. After that we had three emergency c-sections that we weren't able to get this vet for and none of the moms or their kits made it. It could be entirely coincidental, but i'm fairly confident atleast two of those moms would have made it if we got them to this specific vet.
This vet also knows that we know what we're doing and trusts our input as we trust hers.
For us, finding a good chin vet has been a major trial and error. If you're looking for a vet for surgeries you'll want to ask if they've done c-sections, etc. and if they've been successful. We also take into consideration the vets' willingness to take our word on things and listen to us, even learn from us, and if they aren't as knowledgeable with chinchillas but are skilled at surgery, or have the resources we don't have access to, we will give them a chance.
The first vet we took her to aren't *as* knowledgeable with chins but cut us amazing deals and are willing to learn. They are also easily accessible and open more hours than other vets. So we take any chin that needs an x-ray, euthanasia, or simple problems like URI, UTI, eye infection, foot infection, etc. there.
You also really need to educate yourself. And this will come with time and experience. For the basic stuff I listed above, we can go to the vet and tell them "so-and-so appears to have a UTI - can you confirm and give us such-and-such antibiotics?"