Answer: Dust!
Chinchillas need access to chinchilla dust to keep their fur looking clean and healthy. They need to be kept away from open water sources and are miserable when wet. If your chinchilla gets wet, rub them gently with a towel to get the excess water off, and offer them a dust bath.
Below are some pictures of a pet chinchilla of mine named Doughboy. I want you to see the changes your average pet chinchilla will go through.
Doughboy Bio:
Doughboy is a neat guy, he likes to shoulder surf and doesn't mind crowds or going out. He has been to four different shows, 2005 MCBA Boise, judged by Henrika, 2006 MCBA Ellensburg, judged by Jack Humphrey, and 2006 MCBA Boise, judged by both Somovias and Gene Adcock. Recently he was at the 2007 CA Empress show. So far he has taken a first at every show. I estimate his age to be around 16.
Don't be afraid to show your pet chinchilla, regardless of age. Shows are a lot of fun and you always meet some interesting new people.
DB loves to watch me play games and websurf. He'll sit on my shoulder for hours.
The above photo shows what happens to a chin when you pet them a lot. The fur will get a greasy matted look. It will also look like this if you don't dust them enough.