I was thinking about your sitiuation, and you might want to consider calling your local animal control, or fish and game department. In the past when I have had a pest problem I would call them up, and they would let me barrow live animal traps. Once caught they would relocate or disspose of the animal. I would pressume that the preditor now has a taste for chicken and may return.
What type and opening size is your fence? Is the area covered from birds? Hard to help too much but you should crawl the fence and see if there are gaps they're getting thru or if they left tracks and try borrowing a trap baited with the remains of your lost bird. It's likely it will be back for another easy meal.