Mangeo - You cannot house a 4 month old female with a mature male. The female WILL get pregnant and there is every chance that she will die giving birth to kits she isn't mature enough to deliver safely. Not only that, but the toll it can take on her body is tremendous. She isn't done growing. Her bones aren't finished growing. The nutrients she needs to make her body strong and reach her full size and potential will be eaten up by the kits growing inside of her, then when they are nursing they will be sucking even more out of her. Please, separate them and keep them separate. Your chin will survive just fine without a visitor for 3 days a week and the female won't need to die to keep him company.
What about if you guys split a bag of food? Or if you just send food home with her? Since you already have a great food and since she comes to visit (and NEEDS to be in a separate cage of her own), why not just buy enough food for 2 and sent it home with her? Charlie Chinchilla really is about the worst food out there, unless you give your chin bird seed. She would see such a difference in her girl. Also, God forbid, if she is pregnant, Charlie Chinchilla will do nothing to help support the growth of the babies and the health of mom.
As far as them not fighting, just because they don't right this minute, doesn't mean they won't. If he does get her pregnant, and if they are together when she delivers, he will attempt to breed her back. That means just before she delivers, during the delivery, and immediately after - he can get her pregnant again. I've already discussed the toll it can take on a female's body, but many times a female will refuse. The male refuses to take no for an answer, and one or the other can end up very dead.