Can you shoot a chicken in the head to humanely euthanize it?
Breaking it's neck, or just cutting off its head with a sharp knife might be easier (or at least a more "sure" thing). I've made a little gas chamber for rats before. I had them in a bucket, then i had a ziplock bag with backing soda in it, and a small tube that went from the bag to the bucket (with a lid on the bucket). Add vinegar to the baking soda, and close the bag around the tube. The gas goes into the bucket, and the little guys go to sleep, and pass away. Sorry about your poor chicken.

