Can I house these 2 rodents together? Guinea pigs and chinchillas?

I love chinchillas. I have 2 guinea pigs and I love them. Is it possible to house a chinchilla and 2 guinea pigs together? Could they hurt each other? If they eat each others food could they get sick? How are they different from each other? Can chinchillas climb? I won't house them together if they could get hurt or sick from each other. But is it possible? Thanks!