I'll assume the chins are pedigreed and don't carry any genetic issues that can be passed on to the kits. Some genetic issues can skip generations, so you want to know
at least back to the grandparents of the chins you are breeding. 8 months is the minimum age they should be bred, but ideally you should wait until around 1-2 years old, that way the chin is full grow and you can get a better look at how they turn out and if the female is a good size to breed. 3 years old is still very young, chins can live 20+ years and can technically still breed until they die.
I would take some time and research breeding on here, there is a lot of info to know. One major thing to keep in mind with breeding chins though is that it's more risky then breeding other rodents,
a lot can go wrong. Don't get into breeding unless you are prepared for the possibility of losing one of your chins. Females have been know to kill males (and the other way around, not all chins get along), and complications can happen that kill the female during or after birth. If the female dies, rejects her kits, or isn't producing milk, are you prepared to do round the clock feedings of the kits every couple hours for weeks? You also want a minimum of a couple thousand (ideally a lot more) set aside for emergency vet bills, an emergency c-section for example can easily run into the thousands. Do you have a vet experienced with chinchillas? Not just seen them before but has actually worked with them enough to know how to do emergency surgeries and is on call 24/7 in case there is a problem with the pregnancy?
Also why are you wanting to breed? Are you looking to improve a specific color mutation? Looking to get a specific look? size? color? What is your goal? Are you planning to show the chins? If you don't have an idea of what you are going for attend chinchilla shows and get and idea of what other people breed for. You should already know what you are wanting to breed for before buying the chins, so you can pair them properly.