Yes, euthanasia always is a last resort; after I've done everything I know to do for a sick or injured bird, and I'm confident its condition will not improve. (I don't have access to a vet that will see chickens; I've called everywhere in my area.) You don't have to be a good shot at all. Just a little hand/eye coordination to make sure the shot is clean and gets the job done in one go. I've always euthanized after dark, so the bird can't see. They move less in the dark as well. You could also wrap the bird in a towel, if you choose. Have someone hold a flashlight or use a head lamp. Put the barrel to the back of the head (or the side if the bird is moving its head) and fire. It is quick and painless, but the bird does flop a bit. 
 
My original intent with this thread was to see if there was a good way to basically put the chicken to sleep, but after the responses, I really think the .22 is the best and most humane way to go. It's quick, painless, and the birds often don't even see it coming.