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.
Grooming * Show Clubs
You should have already reviewed the section on Dust baths -
Grooming for chins can be as simple as keeping up on the dust baths. This is important, even more so when the tempetures and humidity are high.  My rule of thumb is 2 baths in a week during normal weather.  Once every 10 days in very dry winter weather, and every other day during those hot humid Iowa summers.

If your chin has small areas that are matted, use a bit of corn starch, rubbing it into the matted area prior to the regular dust bath..... If an area of the coat is excessively dirty or stained, you can use a bit of baking soda, rubbed in to that spot just before the regular dust bath. 

Additional grooming can be done prior to the dust bath by a gentle combing of the coat.  Use a number 3 or 4 grey hound comb.  If that is not practical, which it is not for the normal pet owner, then you can use a regular human comb, the coarser side of a regular 7 inch plastic comb.
The only purpose of combing is to losen dirt, lift the hair, prevent mats and allow the regular dust to penatrate the coat.  If you start this early in life with a chin, it will be easier for them to accept. But any chin will learn to cope with it, just start slow and work up to doing the entire coat. (pictures are in the planning for this procedure)
  Use the comb to lift the hair starting at the bottom of the hip or at the butt, and run gently up to the spine. Run up the sides of the body, again to the spine,,, from the base of the tail and up the spine. 
Be very slow and gentle.
The shortest hair on the skin of the chinchilla is at the nape of the neck.  This is the point you want to be combing (lifting) all the coat towards and along the spine. Fluff the hair on the belly too, to make sure there is no mats of tangles.  Then let the chin bath as normal. 
Do NOT try to do all these things (combing, corn starch, baking soda) on the same day.  Always finish up with a dust bath as this is very calming for the chin.
DO NOT try to comb ALL the loose hair off the chin, as if you do, you will have a bald chinchilla!

It would benifit any chin fancier and keep to contact a local member of the MCBA to become more familiar with the hobby, and maybe attend a show.  There is a wealth of knowledge with any group like this that goes beyond anything you can learn on the internet or from pet shops.

Other groups, like 4H, are also of value to the novice chin keeper.