I own three cats and have had up to 30 chinchillas in my house at one time. Although my cats have never shown any malice towards my chinchillas and have not harmed them when the chinchillas have escaped from the cages, I would NEVER let my cats and chinchillas out in the same room on purpose. I do allow my cats into the chinchilla room when all of the cages are locked. However, I do know what I am risking in doing this. If one of the chinchillas got hurt or killed, I know that it would be my fault and not the animals. Unfortunately, people allow their animals to be together and, when one of them dies, they blame the animal and often start neglecting it or get rid of it. As animal owners, we all make decisions on what we think is best.
My advice is this: Do what you want to do with your animals. But know that it is NOT the animal's fault for behaving on their natural instincts. If your cat kills your chinchilla, chalk it up to a lesson learned on your part and love your cat just as much as you did before the incident.