Health
Prolapsed Intestine.
Veterinary assistance required. Do not attempt to treat this yourself. Worst case scenario is intersusseption (I have only ever had one chin that has had this happen. It is very rare), where a part of the intestine further in from the anus prolapses requiring surgery.
The closest comparison that I can think of is a sock turning itself inside out. The neck of the sock representing the anus. In a normal prolapse the area just above the anus quite literally drops out of the poor chins bottom. In intersusseption, imagine the heel of the sock being pushed out. The vet will differentiate between the two by inserting something like a pastette into the anus to the side of the prolapse. In a simple prolapse the pipette will only enter a short way before it is blocked, in an intersusseption it will enter a fair distance before it is blocked. To correct the first is a fairly quick and easy procedure probably requiring a few sutures to keep the intestine in place i.e. inside the chin, with an intersusseption the chin will require general anaesthetic and major surgery to return the intestine to the body cavity, unfortunately without any sure guarantee of doing so without twisting and therefore blocking (torsion) the intestine. From the financial point of view we are talking serious money here. I had to take one of my female chins to the vets with an intersusseption a while back, the vet warned me that the total bill would likely be in excess of £200, and would more than likely still end up with the death of the chinchilla. His recommendation was to put the animal to sleep, especially as she had been chewing on the protruding intestine before I found her.
It is possible to shrink the prolapse using a strong sugar solution. Coat the prolapse in this solution having first cleaned any fur or dirt from the tissue. This should work fairly quickly (up to 30 mins), and may allow you to replace the prolapse (gently). Again always seek veterinary advice. Do not attempt this if you are unsure of the process or degree of damage or prolapse.
The chinchilla should be put on a low dose of atropine to slow down gut motility. For the next two weeks keep the chin calm and quiet, and on a bland soft diet of something like baby food and cereal. When the sutures are removed gradually return to a normal diet.
Unfortunately even after the vet has treated the chin, this is likely to happen again at a later date. It can not be permanently repaired and treated.