Part of what makes this Gears of War 3 Easter egg so fun is that it's a stark contrast to how serious the series takes itself. The other part is that it's a gun which fires live, exploding chickens.
The Cluckshot, a fowl-centric take on the Boomshot, is a secret weapon that can be obtained in single-player on Insane difficulty. The method itself delves into spoiler territory, so I'll point you to GameFront's video walkthrough and say nothing more given how recent Gears 3 still is. Wonder what other surprises are hiding in there.