I am going to preface this with, I have never had or been around a chinchilla that is that aggressive or bites that hard.
That being said my advice would be that if they bite your hand when ever it is near them get a leather glove and let them go to town. Once they learn it does no good they should backk off. If its just when handling I would start by just sitting next to the cage and letting the chinchilla run over my hands, to acclimate to the way they look, smell, feel and move. After they became comfortable with that I would gently hold them for a moment after they jump onto my hands then release them, so as they may realize I am not going to hurt them by handling them. I would make the time I hold them steadily longer over the course of a week or so until they are comfortable with the aspect. I would never expect a chinchilla to enjoy being held.
Look, Smell, Feel, and Move-
These in my experience with animals are the most important things to getting an animal comfortable, from horses to chinchillas and they have to be introduced in that order and it has to be on the animals terms as to when they become comfortable. The last one is the most difficult and the most important.
I mean, think about it, hands are weird! all the digits move. Often simultainiously and in more then one place! Oh the insanity of it!!! I cannot get used to the way spiders move and thusly do they creep me out. I don't mind them if they are sitting still but the moment those legs go into action.... Eeep! I can only imagine its similar to chinchillas, and not only do they move weird, they are big, and they want to grab you....
Just my thoughts.