I have two Siamese cats, and then got a chin. I know my two well enough to know that he's too big for them to be interested in (this will not be true of all cats), but they're still not allowed in the same room (I have to be careful about this since my male cat can open doors, so it needs to be locked) even when he's in his cage. They saw him in his carrier when I brought him home, and looked deeply puzzled 'What is it?' and then totally disinterested and unimpressed 'Sigh, is there any point to these weird things you bring home?', but that's the closest they've been to him. I might be confident they wouldn't touch him, but I'm not going to risk being wrong, and animals are not 100% predictable. I don't trust Siamese ingenuity either - my female cat worked out how to open my Russian hamster's cage (not easy) and got her out, luckily we realised quickly and the hamster was unharmed. Most cats also naturally carry pasturella, which is harmless to them but dangerous to chins, and it simply isn't worth the risk. There's also the possibility that a chinchilla, a prey animal, will be stressed by the presence of a predator, though obviously it depends on the chin. It's not fair to a chin who is stressed by it to have predators around them, though.
Cats vary in how much of a hunter they are, and what prey animals they're interested by (my Mario isn't fussed much by rodents but fascinated by birds, but luckily can't catch them, my Tosca is unfortunately an efficient mouser), but kittens are generally curious about and want to 'play' with everything (and don't keep claws in even if they're not actively hunting), so I really wouldn't want a kitten around a chin. You can still take the kitten, just keep them separate.