3 weeks is probably a good time to start with some training but don't rush it. Most chinchillas do not tolerate being handled. When she is in the cage pick her up and hold her for a few seconds and then put her back into the cage. Do this a couple times of day at random times. Do not neglect your normal interaction as it will be stressful at first. After a week of doing that you will see improvement and you can do it more often and hold her longer.
3 months is a very good age to have a chinchilla and to start handling them. If you don't do it enough they will never get used it. I got mine at three months and he was not very tame. I couldn't hold him more than 10 seconds before he would try to bite. After about three months of working with him he was safe around kids. Today, 2 years later, he will sit still on my lap and allow me to cuddle him and at times he craves attention.
When holding your pet do not allow her to flail around. She is capable of causing herself great injury. When securing her it should be either all or nothing. Holding her at the base of the tail can help you with control but always use two hands. Never snag a leg when handling. Always one hand under the chest and the other under the back feet or the base of the tail.
If you get bit try not to instantly react if possible. Learn to control her head. At first you may experience some fur slip so make sure she cannot slip out of your hands and get hurt. Always release your chinchilla at the floor level of the cage so she cannot fall and get hurt. Even a few inches can result in injury if she panics. She will probably fight and struggle at first but you should see marked improvement after a week and should be quite manageable after a month.
In 6 months you should be able to do a lot more with her. After a year I was able to put mine on the scale for his regular weighing (I weigh mine
every day) and he will sit still on the scale without having to use a travel cage. After two years I can set him on my chest and he'll lay down to get scratched. It is a process and you will probably make a lot of mistakes. Just make sure your friendly interactions outweigh the stressful ones and you'll do fine.
