As everyone is saying, it can go most anyway with a chin and any other pet you may have ... depends on the chin and on the pet.
We use to have a cat, Snuggs, he loved to set and watch them, but never offered to go up to them in the cage or while out playing ... of course that could be because one of the chins use to take aim at the cat with the Jumbo roll around and Snuggs would have to move or jump up in mid air, allowing the chin to go under him, rather than through him.
Then, there's Lady, our oldest (3 years old) Great Dane ... she is my chin-setter and helps watch the chins as I change the cages and will not let them hop out during the time the soiled tray comes out and a clean one goes in. She just rests her nose on the edge of the ledge, right next to the opening ... if one of the chins tries to get out ... she blows hot air on them with her breath. She has even allowed little ones to climb in her mouth ... she just keeps it open until they climb out (see the chintoons on my website) ... her favorite time is at night ... she goes from cage to cage sticking her head inside each one to get her night-night chinnie kisses. When we would go out, she use to open one cage (not always the same cage), let them out to play with her, then as soon as we got home she would let us know there was a chin loose, from which cage and where it was. It took us three months to realize she was the one opening the doors to let them out when we were gone. She will even put her paw down on their tail and hold them in place till we can get the chin. Most of them will go to her just as quickly as they will us, if not more so, in some cases.
Now, there's Raven, she's a 7 month old Great Dane ... I don't trust her around the chins ... she plays to rough. She has never shown any signs of wanting to hurt one, but, she will have to settle down more before I will trust her to be around the chins. The fact that Lady will stay between Raven and the loose chin is a warning we listen to.
Buster is our pom, he tolerates them, but ignors them.
Like I said ... depends on the pet and on the chin.
The one thing you always have to keep in mind is that chinchillas can catch almost any illness most other animals can, but chinchillas do not get vacinated or have a natural resistance to these illness ...therefore, what might make one animal just a little sick, can often kill a chinchilla. Also, an animal can be the carrier of an illness without showing the signs of it.
Jo Ann