How wide is the gap in question, a pix would help us identify the problem and possibly offer a solution. Most predators can climb, especially a short height like 3 feet.
I know you just joined today, so you do not have your location in your profile, or your post.
Lets assume you are in North American Continent.

A raccoon is a possibility, biting the head off, but usually eats more than just the inside.
An opossum, does like to eat the inside , from the bottom on chickens, but usually does not bite head off.
If you have weasels, fishers, or mink, I'm not sure how they eat their victims.
First, and foremost,,,,,,,,,, secure that open gap so you do not loose any more chickens. Predators are known to return where there is a supply of food.

WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, and
