There's a lot of legal grey area here I'm afraid.
If these are someones pets, then it's illegal in all situations. The best thing to do is to send the owner a certified letter (where they have to sign for it) to explain the situation. Then they can't say they didn't know.
Then contact your local Humane Society. There are leash laws for all pets, including cats in most states. So the owners letting them roam free may be against the law. At this point, someone who has legal authority contacting the owners will probably get their attention.
If that doesn't work, set up a motion activated camera (fairly cheap) to try to catch the cats in the act. While it's defiantly possible that a cat may be doing this, you might be surprised to see it may be another predator.
If you still catch the cat doing this AFTER you've followed the law and you have proof, you can easily take them to court to force them to replace your animals.
Either way, it's really not the cats fault, so I would have a hard time justifying your taking your frustration out on the cat, as opposed to the owner. Even if you did kill one cat, you'd still be out of a chicken, and the others would still try to get them. This is why cats should not be allowed to roam free.
Just don't go out guns blazing and kill these cats when it's the owner who should be held responsible.
Don't let the nay sayers get to you.
Let them whine all they want about the highly invasive non native pests that are cute little kitties and not shooting them
Its your property and yes you can shoot them since they are a threat to you poultry. If the cats have owners then its their own fault for allowing their cats to roam and getting shot for damaging or killing your property. In fact you can sue the cat's owners for it.
To the whiners, its the OP's private property, the cats have no right what so ever to be on it. The same goes for people who allow their dogs to roam then whine when the dogs get shot.