I have only come across this problem once in 14 years. With me, it was with a male charcoal kit who I aptly named Piddle. At the time I rang around lots of experienced breeders to see if anyone else had heard of this problem, and only found one other breeder (Brenda from Brenvics Chinchillas) who had dealt with a similar condition (I have since heard of several other cases in the UK in the last 2-3 years).
I have also recently read of the condition in a 1960's Ranchers Handbook, where the kits are described as "wetters". It appears "wetters" were first documented in the 1940's on a ranch in Virginia, USA.
It is basically a genetic deformity of the urinary system, resulting in incontinance. The entire belly is usually soaked in urine. It is incurable, sadly.
I did try to keep my affected kit comfortable by ensuring that his fur was clipped away from his bits, as it was only getting soiled and matted. Then I washed his belly twice a day with a mild antiseptic solution (hibiscrub), diluted in warm water. He was then thoroughly dried with a hair-dryer on a cool setting (bought especially for him). I then applied some Sudocrem cream on his skin, as he was getting sore (urine scald) with his incontinance.
I did take him to see a vet, who said that there was nothing that he could do to help (as a chinchilla is too small to perform a "re-plumbing" operation on).
Piddle became so miserable (despite my best efforts to keep him clean and to prevent his skin from becoming urine-scalded) and it was decided to have him put to sleep. It is not much of a life to be continually soaked in wee!!
Hopefully this genetic condition will remain rare, but a rethink of breeding practices needs to be carried out if it crops up regularly in any breeding herd.
N.B. Mild incontinance can also be caused by infection (i.e. cystitis) or bladder stones. Veterinary treatment/diagnosis is essential. This type of mild (temporary) incontinance usually clears up on recovery. | 
