I don't have any experience with chinchillas, but to me the nicest small animal (if you can get past the thought) are pet rats. When my son was in 3rd grade, his teacher had rats as pets in the classroom and she told us how nice they are, don't bite, etc. We were a little squeamish at first, but we ended up getting two rats for our kids and they were great. We had tried hamsters and gerbils in the past, but you couldn't really get them out to play with them, and they would bite. The rats never bit unless you tried to stick your finger in through the bars of the cage (I think they thought you were poking food in to them). You could handle them, too, because they weren't as squirmy as hamsters and gerbils.
And by the way, rats are like cats, always cleaning themselves. They're very clean animals.