I don't like the idea of guns to kill chickens. Not that there's necessarily anything wrong with it, but there are a lot of issues with it as well. I considered it, but decided there were better ways. First of all, a gun of any caliber will effectively do the job, but there are other issues. Please know that I'm not talking down to anyone who uses this method. I'm just offering an opinion from someone who knows guns, and is trying to learn chickens. Some of these are very minor issues, but here's why I personally don't shoot my birds.
-If your hand moves or the chicken's head moves, you either miss or take a chunk out of the chicken's head, leaving it alive. It seems like people who are nervous about killing the bird often go with this method, as it's less personal than chopping off a head, which increases the risk of a nervous, shaky hand.
-When you hit them square in the head, it can be messy. Expanding gasses and high velocity bullets can do amazing and disgusting things to flesh and bone.
-Why have unnecessary bullets flying around? Even a .22 bullet goes a LONG way.
-For a chicken headshot ANY bullet is going to be overkill, yet a BB/Pellet gun won't effectively do the job.
-Anything but a .22 is loud and WAY too powerful.
-It takes a bit of time to line up the shot every time with a live chicken.
-You're spending money for EVERY chicken you kill, when other methods cost nothing.
-You're introducing lead and burned powder into your birds. The bullet going into it's head, and residual lead from loading the gun on your hands when you clean them.
-At the end of the day, it's just not any MORE effective, MORE humane, or quicker than head chopping, and can often be less effective with a misplaced shot.