Things to know about your pet chinchilla
Disclaimer - The following information is provided by the site owner as the practical  application of chinchilla husbandry as I have learned it, in theory and practice.  There is no warranty or liability for the contents of these pages.  It is my opinion and is merely offered as a suggestion or possible solution. All information is solely that of the site owner and no ammends will be made.
Training and Taming your chinchilla
Still a work in progress
The best way to get into a chins head is through their stomach... YES, I know that is not really correct anatomy, but the one thing they seem to understand it food.
Once you have frightened them, they will remember it for a very long time.
They really thrive on routine and monotony - that teaching them something is really done by repeating the actions over and over.

Now, take those three things and you will have what is needed to teach them what you want.
Food rewards, or giving them some treat (even if it is a piece of paper to tear up), or just a nibble of sweet hay.... they will enjoy it. Giving the TOO many treats that are unhealthy... so you have to do it over a period of time.
Be very careful not to frighten, or give ANY First let me say that that way to a chinchillas heart is through his stomach.
Second, chins will not respond to negative reinforcement.
Thirdly, I dont know if the word "training" really applies to a chin,.... definitely not like it does to a dog or even a horse.
Treat are funny for the owner, since the chin will soon learn to respond to you handing him a tasty tidbit, All my adult chins (I have 19) come to their names because I conditioned them with treats. They range in age from 2 years to almost 15 years! Now, most pet chins are fed way too many treats, and pet chin owners can kill the chin with kindness. What to do? Cut out the sweet treats and all the cute-sey stuff the pet industry shooves down the throats of consumers. So, no more then 1 (one raisin a day) and none of that processed treaty stuff. Instead, condition you chin to enjoy healthy stuff like plain Cherrios and bits of plain Shredded Wheat cereals - they can have 10-12 cherrios in the course of a day. Even bits of hay, a sunflower seed or two (a day) or a bit of unscented tissue paper all can serve as a fun, exciting treats for a chinchilla.
You could explore the "clicker training" method as I know a person that tried this starting with a very young chin and it worked pretty well.
When you get a response you want from the animal, give them the reward (a click or the treat... what ever).
You can not correct the chins behaviour with punishments. I know a lady the tapped her chins nose for doing something, just once and he was put off for months and would not allow her near him, but would sit and groom her husbands beard and ride on the sons shoulder, but would have nothing to do with her. Took her almost a year to fully gain the trust back.
I am not sure what you want to train him to do, but you have to take it all in very small steps, break it down and take it slow, rewarding the baby steps as he improves.
Mostly, you have to give him time to be a chin, adjust to the pulse of your home and when you change up something in his world, be aware this could affect what he has learned so far...
Once you make a connection are really understand each other, you will progress faster... older chins (past 8-9 month) will learn much slower and chins that were socialize early (before 3 weeks old) will learn easier. But remember, like people they can all be individuals, do never give up!negative reinforcement.... take it slow and let them show you the way.
Do the same thing, say the same thing, and move in the same way during each training session. As time goes on, make the do just a bit more in order to get the treat.... add on slowly as time goes on.....

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