Check with local animal control officer . They may have a hav-a-hart trap that you can use to trap the critter. If you do trap place a burlap bag over the trap and gently remove. Animal control will have suggestions as where to transport it or they may just relieve you of it. Be very careful skunks have been know to carry rabies and definetly put you and your family at risk.

Thanks for the suggestions Edwin! My husband is working on fixing the fencing today and we'll see if our visitor comes back once he realizes he can't get in.

I have even more chickens that you do, so I have some experience. Do try to trap it, and then get husband or another guy past puberty to pee all around the fence and area. I know it sounds weird, but the smell will deter a normal predator. I have an unfixed dog that does the trick for my hens. Put some logs or felled trees around the edges, keeps digging at bay. I don't have to do too much, thanks to the dogs.

You know, I caught my husband a year or so ago peeing outside and he told me the same thing you did! He does this regularly and it hasn't work with this one skunk but he fixed the fence yesterday and there was no sign of our stinky friend last night.

2 Tablespoons Codliver Oil
1/4 Cup Liquid Ivory Dishsoap
1quart of water

Spray liberally around entry sites.
That should do it -Caveat:
The skunk will probably scent the area in retribution the first time
but will likely visit elsewhere thereafter. Worked in our yard.

ps. Don't be alarmed at the site of a skunk-a simple 'shoo' will send them away-as long as you don't alarm it (except young'uns)
they haven't learned self control yet. Grownups will save that scent for when it is needed.

Oops!
That should have been Castor oil.
Not Cod Liver
For those who may be wanting to try it.