Raw chicken bones are fine. Cooked ones can choke cats. Cats choke or get things stuck in their throats as much as dogs do. There are a couple of things you should never feed your cat:

1. Cooked bones - Any kind
2. Too much fish - the oil in some fish called sterate can affect a cat's liver - tinned, raw or cooked
3. Human milk - most cat's cannot tolerate the lactose in milk so always give them lactose free cat's milk
4. A vegetarian diet - cats cannot produce a chemical called taurine (unlike dogs) they need meat to get that essential ingredient unless they are getting it through specially formulated cat's milk.
5. Chocolate and onions - this can cause kidney problems in cats as there are certain chemicals in both that cannot be broken down by a cat (there are others these are the worst offenders)

I would take your cat to the vet and get her teeth checked out - it is not uncommon for cats to have tooth related problems such as decay. Hope this helps and best of luck.