This thread got me thinking .... I used to go with a friend of mine out to a place in E. Colorado and shoot prairie dogs for fun. It's a whole sport, and the magazine Varmint Hunters (or was it Varmint Shooters?) was devoted to, basically, killing for fun. Coyotes, crows, p-dogs, ground hogs, you name it. Sounds pretty sick, huh? So, I was thinking, wow, what's the difference here? And I realized, I've never heard of a varmint hunter, read about a varmint hunter, seen a varmint hunter, want the animal to suffer. It's all about instant turn-off, if possible. Varmint hunters shoot animals that can be killed justifiably - the p-dogs make holes that cattle step in and break their legs, the coyotes are preying on sheep or local pets, the crows are causing problems, etc. In effect there's a sort of "formal declaration of war" against a certain population of certain animals that goes through our heads, plus, we try for a quick, humane, death for them. We like to think it can always be a quick, relatively painless thing. The stuff the serial killers do, well, let's just say they do not want the animal to have a painless death. That's the HUGE difference.
I'm going to guess you have someone very weird in your area, or, and while it sounds like a long shot it may be, you have someone who's really annoyed by the sound of your chickens. I was rooming with a guy a couple of years ago who was really ticked off by the sound of a rooster that must have been 2 blocks away. It was stupid, you could barely hear the thing. It's still a SICK way to show their annoyance, so in that case you still have a pretty strong creepy factor here.
You can't shoot anyone over a chicken. They have to be a threat to YOU. You have to just document everything and work with the cops.