Sounds like you found a likely explanation.
Have you noticed this problem before?
What kind of surfaces in the cage does the chinchilla rest on? If all he has to sit on is wood shelves it may need some bedding to rest on. If there is urine on the shelves or built up on the wire floor this can cause irritation.
What kind of bedding are you using? Carefresh bedding can leech out the oils in the skin making it too dry. Pine bedding is your best option for use inside the cage.
Has your chinchilla been on medications recently? What about new or unusual treats or foods? Sometimes allergies can cause this.
I've seen cases like this on the board. Sometimes they are ongoing and sometimes they just go away on their own. Sometimes making adjustments in the cage can help. It is a manageable condition. Unless there is active bleeding or obvious cuts or open wounds you don't have much to worry about. I've seen cases where there was blood spattered throughout the cage from this so don't panic if it gets worse before it improves.