There's also the broomstick method, what I prefer for dispatching old friends, it's less bloody than the chop. Take something like a broomstick, hold the bird by the legs, place her neck under the stick, hold it down firmly with a foot on each end, and give a firm strong yank on the legs until you feel a crunch as the neckbones give. The bird will die instantly, but give reflexive flaps for a few minutes afterwards. You can walk away, or cover the bird with a blanket or bucket if that sight bothers you.
Another thing that might help is to find another chicken keeper in your area with whom you could trade difficult dispatching chores. It can be easier to focus on doing the job efficiently when you're not so emotionally attatched to the individual.
I'm sorry for your dilemma.