Sick or Injured Chicken help?

I have a bird with a presumably bad leg. She just sits there and so we isolated her in a smaller cage away from the flock with food water and bedding. I think the time has come (as she's just getting worse) I can't stand to watch her just die and I can't do the culling myself. Is there a more humane way to put her down than chopping her head off? I guess we could do that and eat her but I'm not sure if that's the best. Has anyone ever "humanely euthanized a chicken?