Holding your chinchilla: First and foremost you need to know a little about your chinchilla if he/she is new to the family. Ask the pet shop or previous owner if your new chin is used to being held. This will give you a bit of an idea of what to anticipate when thinking of holding your chinchilla.
Think of it this way, a big strange person just took you from an already strange place, on a rough and nerve racking ride across town, and now you are trapped in another unfamiliar place with little to nothing that makes you feel at home. - Now is NOT a good time to go and try to hold your new chinchilla.
Once again you need to take in mind that all chinchillas have their own personality so some chinchillas may warm up to you quicker, some will take a while; furthermore some will like to be held and scratched behind their ears and other will possible never be keen to the thought.
The most important thing is to make your chinchilla feels safe in it‘s cage. You should not try to hold them for the first few days, maybe even the first week. Let them get used to their new cage and they will then think of it as not only their home but also as their safe haven. (not to mention the place in which their food is located) This will be important when you begin to let them out for a little play time (exercise); as even if they are not ready for you to hold them, they will still return to their cage either when they feel in danger or go looking for their food.
In these first few days another thing you can do is let the chinchilla smell you each time you give it food, of course giving it treats is a great time for it to smell you as well but remember you do not want to give it too many treats. (one trick is to break the treat into smaller pieces) Doing this will show the chinchilla you mean them no harm.
When you feel it is safe enough to let the chinchilla out of it’s cage to play sit still while he/she runs around. (NEVER CHASE THEM!) They are curious creatures and at some point they will run over to you to ‘check’ you out. If you think the chinchilla is ready for you to try and pet it, move slowly and keep your hand low. Then again if they are too skittish to let you hold them at this point and play time is up, you can always coax them into their cage with either food, treats, or even their dust bath.
After much trust in their part and patience on your part, you can get to the point in which you may hold them. DO NOT GRAB THEM AROUND THEIR STOMACE/CHEST, as they have small and fragile bones. Your goal should be to kind of ‘scoop’ them up. Chinchillas feel safe when they feel something solid under their feet so try to keep this in mind. If you need to ‘grab’ (such a bad word to use here, just remember to be gentile) them in order to control them till you get you hand under them you can grab them by the base (Not the TIP!!) of their tail. This does not hurt them, but keep in mind you do not want to move quickly or stress them out. (I personally rarely had to grab my chins by the base of their tail as they did not like the idea of my hand coming from behind them and it was easier to approach them from where they could see me and not be startled.) Try to be sure your hands are clean from dirt and oil.
There are a couple extra things you should know about. For one, when a chinchilla feels scared/in danger/stressed they will shed their fur in clumps. So when you see this, back of a bit and give the chin time and space to relax. Second, when you are holding your chinchilla, not only keep support under their feet but also hold them close to you. (if you can hold the base of their tail in-between two of your fingers while supporting them from underneath, this will keep them from trying to jump down)