Chinchillas are not as docile as other pets like guinea pigs or rabbits. They need to be handled regularly and socialized because their natural tendency is to find a dark place and hide. You're going to have to start out by jumping in and just making it happen or this problem will only get worse. I recommend short sessions. Just take your pet out of the cage and hold it for about 10-15 seconds and put it back. Use proper restraining technique. This means support the chinchilla's back feet and secure the base of the tail. If it tries to bite you support under the jaw. This might happen the first few days until your pets get more used to being handled. You can suspend by the base of the tail if you are afraid of dropping it. Absolutely do not handle further down the tail - only the very thickest part of the base.
After that time play with your pet through the bars of the cage or in the cage so you have some positive interaction time, and then do it again later in the day. Chinchillas usually like to be scratched under the chin and think they are being groomed. This can also have a calming effect.
The chinchillas will learn that being restrained is not going to hurt them, and that they are not always going to get their way. This should be part of their daily routine. After a few days of this you should see your pets becoming more calm, and you can incrementally increase their time being handled. Be careful not to overheat them because they are going to squirm and fight at times as they are learning. Eventually your pets should stop trying to fight you and might even crave being picked up, although that can take a few weeks. My pets can usually take it or leave it but both can easily be picked up and carried around without showing any signs of stress. At times they will jump into my hands to be carried around.
Be extremely careful not to drop the animal onto any hard surface. Try to release at floor level. If the animal is fighting you be certain you can control it before removing it from the cage.
