The bad thing is, you don't know the health of the wild chicken. She could have a disease or bacteria your chickens aren't used to, making your chickens sick. Plus, the wild chicken will have a hard time come winter. I would attempt to catch and either find the owner, or, isolate the wild hen (assuming you can catch it) for 30 days and then integrate. Chickens need companionship and something to eat and drink come winter. I would attempt to be proactive to protect your flock from potential disease and to save a chicken that cannot take care of itself when bad weather comes. She will not make it through winter. So, if you cannot catch her, you might need to be more drastic. It would be better to shoot and eat her, than take a chance on her bringing disease or watching her starve through winter. The lord provides, sometimes in odd ways. Might mean a free pot of chicken and noodles.