The article on using carbon dioxide is a good one. I read a couple months back some discussion on it. A few reported some problems-didn't work, even though they followed directions carefully. In this thread, auto starter fluid was also mentioned. I helped a friend use starter fluid with a very sick rat. It worked pretty well. I put some cotton balls in the end of an empty toilet tissue roll, taped the end, so the cotton balls wouldn't fall out. Soaked the cotton with starter fluid and my friend held the rat with the open end to the rat's nose. The rat didn't like it a first, then tried to go into the toilet paper roll, then relaxed and died.
Later, thinking about how to improve this, it occurred to me that NO (nitrous oxide) is used as a propellant in whipping cream (the kind you get in a can, say, Ready Whip.) Dentists use NO to calm patients-I believe it is also called laughing gas.
I'm not sure how practical NO would be for a full sized chicken, but for those of us with very little chicken/farming experience, I though worthwhile to consider. Anyone with any experience with NO to calm a chicken before euthanizing?