Once you have your chicken house all secured so skunks can't get into it, you may consider moving the chicken door that lets them go to the pen up a couple of feet off the ground. Then put two simple ramps made of boards on the inside and outside. Chickens don't mind climbing the ramp, but skunks don't seem to be able to figure it out.
The best way to get rid of skunks, without endangering other animals (like cats), is to catch them in a live trap. Personally, I hate the idea of leaving out poison. Once you've caught a skunk in your trap, throw an old rug or blanket over the trap, wait a little while, then pick up the trap, rug and all, and take it somewhere you can release the skunk, or shoot it. Don't shoot it in the trap. It will squirt its stink all over your trap if you do.
Also, most of the time skunks just want to eat your eggs. But occasionally I've had chickens killed by them.
