From the experience from my 2 chinchillas OLLIE and OPTI
Step 1: Training 1
The first step to training a chinchilla is to bring them into a space were they can run around and play. Make sure there is a spot were they can hide.
Step 2: Training 2
The next thing to do is to patient. Wait for your chinchilla to do something or make a move. Make sure there is someone in the place with him or her at all time. Just wait for the chinchilla to get used to its surrounding (this may take no time at all or a really long time). PS:the longer the better
Step 3: Training 3
After the chinchilla get used to its surroundings it's time to bring out the treats. I recommend papaya or something you know they will like. Quietly show the chinchilla that you have the treat. After, place the treat next to his or her hiding spot or were ever he is always near. Then wait for your chinchilla to take the treat and eat ( this also may take awhile).
Step 4: Training 4
After repeating step 3 a few times the chinchilla should gain more trust in you. So now start hand feeding him or her the treats. Do not hold the treat in the palm of your hand hold it with your thumb and pointer finger and reach out to the chinchilla. Once it takes it repeat it also a few times.
Step 5: Final Lesson
Once he or she can eat out of your hand only reward him with a treat if he or she does something good or something you want him to do. After bring him back to his cage and make sure he or she eats a lot of healthy food because it ate a lot of treats which is not good for it. Then skip a day and repeat the process until the chinchilla has gained full trust in you.