I am not exactly sure. When my mother had her 2 guinea pigs, we threw a rabbit in their. She was small at first and grew bigger. Our male guinea pig (Getting no action from the female) attempted to mate with our rabbit and failed. Upon trying more, we later found our rabbit bite part of our male's guinea pigs ear off!!
I wouldn't suggest it, especially if the cage is smaller and cramped, chinchillas can be big.
I would not put them in the same cage. Your guinea pigs will have different needs than your chinchilla. Guinea pigs tend to be a very defensive animal, meaning that they tend to try and protect themselves from anything they are not familiar with. Guinea pigs also tend to be the type of animal who is more likely prone to stress when around familiar surroundings. They need plenty of room and familiar surroundings. Too much stress can cause your guinea pigs to become ill or even die.
I would highly suggest getting a separate cage for the chinchilla.