Just to put my two cents in
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I totally agree that this animal just be neither bred nor neutered. If you don't know the animal's genetic background (his parents, grandparents, etc) then you could end up breeding chins that have genetic problems you don't know about, and producing chins with the same hereditrary genetic problems. Many of the most common genetic problems can and often are life-threatening and extremely painful. The animal would most likely end up being euthanised, but only after an owner has become attached and has to go through the heartache of that decision. Also, remember, any animal you breed is going to be associated with your name. You don't want to get a reputation as a breeder who produces inferior chins.
Neutering is a bad idea as well. Surgery is always very risky for chins, as they tend to do poorly under anesthesia. So surgery is something that should be avoided unless absolutely necessary.
I understand the allure of having chinchilla kits around, and the concern that his behavior might be embarassing or awkward to deal with. It's possible he is mounting as a show of dominance or excitement, and this behvaior may diminish or disappear entirely over time. However, since this is your first chin, you should consider taking some time to really learn about breeding, before you do it. It's a lot of fun, but any breeder on here willt ell you it is also a LOT of work and huge responsibility. Responsibility not just for the care of the animals, but for the QUALITY of the animals we produce. We have a responsibility to understand the genetics and biological processes at work in our chins, so that we can produce the best, strongest offspring possible.