Remember, the instinct to stalk and hunt small furry animals is a dog thing, not a breed thing. They get that from their wolf ancestors. Some breeds have it stronger or not so strong and even within a breed, some individuals have it stronger than others. Some breeds have more of the predatory motor behavior sequence than others. In other words, some dogs will just eye & stalk, some will eye, stalk and chase. Some will eye, stalk, chase, bite/grab. Some will go onto the kill and dissect. Most dogs do not have the entire set of motor patterns. So, your Chi may be eye stalking and if she could, might chase. Whether or not she'd go onto the grab/bite and kill.....who knows? I wouldn't want to find out. LOL. If they were ever used for ratting, that grab/bite and kill tendency could still be in her.....or it may have been selected against in the breed for a long enough time that it's not such a strong or prominent tendency in most. All of my dogs are enticed by running squirrels and will chase after them. I have a Dobe, two Chi's and a mix. It's mostly a "dog thing."