Do a search on humane euthanasia and you will see many methods. I would opt for what ever you see as the quickest and surest and then the easiest on you. Don't do it too soon and don't do it too late. Watch the chick and make sure it is the right choice, but once you are sure, don't put if off. It is not as hard when you know it has to be done, but it is harder to do the longer you wait and not fair to the chick to prolong suffering because you don't like the idea of killing it. If you just can't do it, find someone who can and make sure they do it humanely.
I have only done it once, and I put the chick in a ziplock bag and put the baggie in a small paper sack. I then put it under the tire of the car and backed over it. I know it was killed quickly and I didn't have to look at it afterward. It was still very hard, but the kindest thing I could do.
