It is a good idea to at least take a peek at that area whenever you have him out. Pet chinchillas are less likely to get them then breeding chinchillas (although it is possible). If you notice a change in that area then you will need to do a real hair ring check. The danger comes when the hair around the penis gets so tight that it can no longer function. Urinary tract infections set in, or in bad cases the chinchilla can't urinate at all. Sometimes blood flow can be compromised. Left unfixed it will eventually lead to death.
Usually when there is a bad hair ring you will notice the chin cleaning/biting at the area more. You may also notice that the penis isn't full retracted into the sheath. If you ever notice anything like that you need to check right away. If the ring is left on too long or is really tight, he may need some antibiotics to clean up any infection.
