Well I guess first of all you would have to have a strong suspicion the tail could be broken. Did someone grap the chinchilla by the tail to catch it or pick it up? If something like that happened and then you notice pain in the chinchilla from touching the tail, yes I would assume the tail is broken. I would also believe you could feel a break, if the tail was laying crooked you would definitely be able to see that. As with anything the only true way to tell if something is broken is to have an x-ray, however I don't know what a vet would do for a broken tail other than to amputate. In any case a trip to the vet would provide pain medication which would be beneficial to the chin most certainly.