Dermatophytosis, also known as ringworm, is a fungal infection of the skin. 1
Ringworm is very contagious and is one of the few things that can be passed animal to animal, or even, animal to human. It can lay dormant for long periods (see What To Do). In chinchillas, having damp skin that isn't dried completely, can cause them to get ringworm. It's environment is warm, damp and dark. A damp chinchilla is exactly that environment.
Typically it results in a red, itchy, scaly, circular rash. Hair loss may occur in the area affected. Symptoms begin four to fourteen days after exposure. Multiple areas can be affected at a given time. 1
Be sure to wash your hands religiously every single time you handle your chinchilla, both before and after! If you have other chinchillas in the same cage, you will need to separate them until the ringworm is healed completely. You will also need to sanitize your cage with bleach (rinse thoroughly with water after) and replace anything wood as well as other pourus items, such as lava ledges. The fungus can hide dormant in these items and cause continued reoccurrences.
1Wikipedia https://en.m.wikipedia.org/wiki/Dermatophytosis" target="Wikipedia