Rattler, unless you want more babies in a few months, put dad in a separate cage (this is also a good idea to prevent biting.) Chinchillas can and will breed immediately after childbirth. Also, I'm told more than three litters a year is more than most chins can healthily bear, so keep that in mind. Make sure you have a big enough sleeping house for mom and the kits (another important part of preventing biting.) Weaning takes place after six or seven weeks, and once the kits have been separated from their mother, they may overeat for a while, so their diet and droppings should be monitored. The kits may already be getting into mom's solid food, which is normal and healthy, but you should make sure she has plenty of hay and pellets. The kits will reach sexual maturity in four or five months, and I think you can sex them after three. I hope that helps some! Your local exotic vet should be able to help you, too, as chinchillas are becoming fairly common pets.
On a side note, just because something is classified in an order with one group doesn't mean it's more closely related to that group than any other. Taxonomy is a human invention which has no bearing on the actual relations of critters. As for chinchillas being rodents or lagomorphs, taxonomists have been debating moving them in to lagomorpha since the 80's, but it's not an easy choice to make - some professionals have even suggested adding a new classification, if I remember correctly.
~Joe