I always hear of all these states or counties with laws pertaining to shooting guns, no guns in town, have to be 100 ft from a neighbors house or whatever. What I say about these laws is that they pertain to hunting or sport/target shooting, they don't pertain to you using your gun to defend yourself or your livestock from criminals or animals, if that were the case then everyone who legally carries a gun in self defense in many areas would be breaking the law to protect themselves or others. You have a right in most areas to protect your livestock, regardless of any anti gun laws.
I would use a 22 or 22 mag at that distance they will kill most anything. A good air gun would probably work on most chicken predators but I just don't like the idea of relying on that.