Speaking from experience in the field, raccoons can pretty much DESTROY a cat trap if they want to. Badgers would take any sort of live trap APART!!!!!!!!!!!!!!!!!! State laws may differ but some animals can and some can't be trapped by other means (other than live trap) without necessary permits. I have NEVER seen a raccoon dig under something to make a den. Not in their usual behavior range. Skunks, badgers, foxes, rats, and feral cats dig under.
Depending on how it would impact your chickens, a good sized rag, like an old towel, soaked in household ammonia can do the trick. Stuff it in the hole with a stick. If you put a hook on the stick you can fish it back out to replenish the ammonia after a couple of days. After a few days of being stunk out, he'll move along. Then you will have to permanently repair the hole so he can't dig it back out. Pavers or something he can't easily overturn with his big claws (skunks and badgers both have large digging claws).
If you're going to live trap, canned cat food works best for raccoons and will also easily catch a skunk. Be mindful that any of these animals can carry rabies. Don't get bitten. If you do get bitten don't shoot the animal in the head as you'll need to have it tested for rabies and the brain will be the tissue tested.
You can sprinkle some flour outside the hole to see when he's coming and going. Skunks and feral cats are more likely to be coming and going nocturnally. Badgers in the day time hours.
Let us know what type of critter you finally find.