Sorry about your chick. I had to cull my first chick last week and it was pretty awful, I did some research on BYC and most seem to use the method of snipping off the head. Sounds bloody but is very fast. A few drown or put the chick in the feezer to die, both those methods seem too slow to me. I opted for CO2, we have a cannister we use for beer making. I put my chick in a box with some shavings, sealed it up as best i could with plastic wrap then put the CO2 hose inside the box. The advice I got was to start slowly so it would put the chick to sleep rather than act as an irritant. She was out within 4-5 seconds, then we cranked up the CO2 higher and left her for a few minutes. When we checked on her 5 minutes later, she was gone. Still sad about it, but I know we did the right thing.
I read somewhere that you can do something similar with baking sode and vinegar, or with starter fluid fumes, but I am glad we have a CO2 cannister. It was fast and my chick did just go to sleep. Good luck with whatever method you use.