I would definitely not recommend breeding her, simply because you don't know her background. She looks very pretty, and may seem perfectly healthy. But she could be a carrier for a number of genetic problems, like malocclusion. If she is, then she could produce kits that could develop malocclusion and be very sick and miserable, then have to be euthanized at a young age. You would do very well to get her a female cagemate to live with.
If you really want to breed I would definitely suggest you go to a breeder, to learn and select your breeding chinchillas. Breeders can usually tell you the animal's pedigree back for several generations. And any reputable breeder will not breed any animal who has dental, heart, or any other genetic problem. This doesn't mean their animals won't ever develop those problems, because sometimes they do just by chance, but the risk of that happening is MUCH smaller.
Out of curiosity, what part of VA are you from?