What is dead? What is alive? Suffering is an but inevitable part of material existence, says the Master...
Sorry.
Seriously though, cutting the head off a chicken is about as quick and humane a death as it is possible to choose, and it's easy to do it right, in the sense that no matter how you do it, you can be assured that the chicken is dead once you've severed the head (reflexive trashing notwithstanding), which can't be said for pithing and throat slitting and such, which requires more precision of technique and a more precise knowledge of what you're seeing. Hence it is often recommended for beginners to use the simple "hatchet method."
Interestingly, in the Middle Ages, and even somewhat later, beheading was the execution method of choice for respectable nobles, because it was considered quickest and most humane. The guillotine of the French Revolution was actually invented to be an improved, more precise, humane and civilized execution method. Common folk, by contrast, were hanged, which sometimes was quick if the victim's neck snapped in the drop but often took minutes to kill, while the victim thrashed and kicked while dangling in the air and slowly suffocating. But truly heinous criminals, such as traitors, were often sentenced to be hung until "half dead," taken down, disemboweled and have their innards burnt in front of them, then have their bodies pulled or cut apart into four pieces. Which is what is actually meant by "hung, drawn, and quartered." Can you say, "ouch?!"
Sorry, I generally don't like to make creepy slaughter vs. execution comparisons since the two don't really have anything to do with each other but couldn't resist sharing this tidbit of history....