We have had multiple experiences with skunks. Last year a mother raised her babies in our barn. She never touched an egg or a chicken. Her babies would come out on the barn floor in the afternoon, and play. All the skunks would walk around with the chickens, and they all tolerated each other. And they tolerated us, and we them. We left them alone because, we had NO problems with mice or rats that year. We only lost one chicken to a skunk last year, and that was a male skunk...and that was because the dumb rooster jumped down and challenged it. Guess who lost.
On the flip side, this year the skunks were back and had a den in our barn. They killed three or four of our large chickens, and also were eating a lot of eggs. They dug a tunnel under the nest boxes and would come up under them when the hen went in to lay. We had an awful time with them but were finally able to barricade them out of the barn. We set traps, but didn't catch any.They were totally unscared of us. If you want to catch them, you're supposed to cover the trap with a trash bag or tarp; this will keep them from spraying. Then, you're supposed to drown them if you want to kill them. You can also buy a skunk trap for around $30.00, I understand. We were REALLY glad we didn't trap any; I don't like to kill things. If you can put something around the perimeter of your chicken shed or whatever building they're getting under, that works. If you can, dig a trough around the building, and fill it with cement. Or, we used thin plywood sheets around the perimeter, which we weighted down with rocks. Obviously, they can't dig through there. Not particularly attractive, but effective. Buried fence would work, too. Also helps to keep other critters out. They will go out at dusk to hunt; then while they're gone, you barricade so they can't get back in. Our problem was, the skunks dug their way in, then that made a way for everything else to get in.