Another easy method is to place the chicken in an airtight container such as a covered paint bucket with a rag or paper towel that has been saturated with starter fluid / ether. This will euthanize the bird quickly and can be used for any size poultry or waterfowl by adjusting the container size. Obviously, you should use care not to inhale the fumes yourself. This method is particularly good for those who are unsure that they would be able to successfully or quickly break the birds neck.
eggchel, that is a good suggestion.
I used a plastic bag and discarged a co2 cartrige (happened to have because I have a seltzer bottle).
It was instantanous, co2 is heavier than air and acts as an anasthetic. Like your method, it was quick, effective, and bloodless.