So my plan is to make a height kill monster trap. I plan on it being a tower half built up on and half dug into the ground with a 16x16 dark room at the top (for monster spawning) maybe wider depending on water behavior. Anyway the point is, how high do monsters need to fall from in order to die.
Better yet, add flowing water at the bottom with only 1 depth. Direct the water into a little cage at the side.
The mobs will still die but the chickens will float into the cage. You will soon have many eggs.