I've hunted chickens for over fifty years, and I've tried everything from 22's to 12ga.
22's are great, as long as you catch them on the ground or perched in the trees and you can get a clean shot to the head, hit them any place else and you're going to make a mess of the bird and lose some meat, and there is not a lot there to begin with.
The other problem I found was, after you take that first shot all his buddies flock off, if you are lucky it might take a couple of seconds for them to figure out he's not taking a nap, and you get a second shot off.
The 12ga #7 shot, is over kill if you're too close, too often I have had to back off to get that first shot on the ground and then hold off on the flying shot so I don't end up with a plucked, gutted and skinned bird before it hits the ground.
The other drew back for the 12ga. is that it's too heavy to carry all day long.
The best gun I've found for chicken hunting was a Franchi 20ga semi-auto. I could carry it all day, next to nothing recoil, easy to point, a joy to shoot on the fly and even my wife liked it, and she is just a little city girl.