I have heard the freezer method before but frankly, I don't think it is as humane as a one stroke beheading. Maybe it's because I'm such a southern baby that I hate the cold, but the idea of shivering for a while, struggling against whatever you are wrapped up in, until the cold finally gets you, just doesn't sound that humane to me...easier for the person to just shut the freezer and walk away, but not easier for the critter in question... just my opinion...
**WARNING....MILDLY GRAPHIC DETAILS FOLLOW - No pics though****
I used a small (handle about 12" long) sharp hatchet, and with the nails in the board it was a very quick and clean kill as I was able to hold on to her body and keep her very still with one hand, while the nails in the board held her head still and let me stretch her neck out to have an easy place to aim. My util sink has a 'rim' about 6" down in the sink where it narrows. The board I used was a piece of 2x4 and it was just the right length to fit perfectly on that little ledge so it was very secure. It was a bit down in the sink, but not so low as to mess up my aim. She didn't even know what hit her - literally - and didn't even struggle against me holding her.
It wasn't the easiest for ME - knowing you are very directly ending this animal's life - but it was probably the quickest and least painful/miserable for her. And was much less 'gory' than I expected it to be. I don't mean to be morbid with the 'details' here, but just posting to help someone else who may be in a similar situation and feels they can't euthanize this way. I'd recommend this method anyday for the chicken's benefit. I surprised myself in that it was much easier to make myself do this than I thought it would be. I knew this morning when I saw the situation was worse for her that it needed to be done and the less time I gave myself to fret and worry over it, the better and easier it was to do.
Frankly, I think this was easier than even taking to the vet for an injection. In an animal that small, often lethal injectsion are done by injecting directly into the heart, as it's too hard to get a vein, and a heart injection is terribly painful, not to mention the stress of travelling to the vet and being handled by so many 'scary' people (from the chicken's point of view). With the heart injection the chicken experiences a lot of stress and then pain - not nearly as quick as the humane beheading methods.
That's just my take on it - your mileage and experiences may vary...