I had a game hen show up in my yard, too! But she keeps to herself, and does not like to be locked in the pen. She lived in a tree for a long time, then when she went broody she moved into the tack room. But I would take her eggs away when I would find where she hides, so she would find a new spot. No roosters here, so the eggs will never hatch. Now she is hiding under the barn, and its going to take some work to get to her, so for now, I let her be. But, she is a loner and does not want chicken friends. She could be with them if she wanted to. She's been here one year now, at first she was very skittish, but she is letting me get closer without having too much of a fit, and the other week she actually ate a few bites from my hand!! We named her Tree Chick when she was living in the tree.