Not sure about seperating Hen from Chicken, but you don't have to build a fancy chicken coop or breeding tower you can literally set up shop in a cleared out Troll Cave, legit.

1. Kill Troll in cave.
2. Place fire on upright stalagmites. (off the ground so they don't burn themselves)
3. Throw eggs down on floor.
4. Wait 2 ingame days or so for Chickens to hatch/grow
5. Seperate them with either signs or cooking stations.
6. Fill any cave chests with Dandelions or carrot seeds.
7. Feed Hens and let the eggs warm by the fire for more Chickens.
8. Profit.