Ah the Chicken Singularity existed before Minecraft patches caused livestock animals to take damage if they were too crowded. Due to the unique way that you could spawn chickens: throwing eggs, you could very easily spawn chickens places they wouldn't normally breed as easily. Or rather, it's hard to breed animals when they are too crowded and overlapping.

So you make a small corral for your chickens. 3x3, 2x2 or 1x1 if you're not here to fuck around. Then toss eggs at the walls (at least 2 high) en masse to spawn chickens. The floor is a hopper to catch eggs and feed that to a chest. Eventually you get tons and eggs and can get hundreds of chickens. Then when you need meat, simply attack the small space they can't flee from and the hopper fills with meat and feathers.

You need this to be loaded for them to lay eggs so they had to be somewhat close to your base. And let me tell you, the NOISE of a chicken farm was something else. Hundreds of bawk-bawk-bawks continuously. Had to mute the game when I did this. Also the load on the server for that many NPCs in a small area was pretty intense and could crash or slow down some servers.