I just got chickens in my current playthough, and I started them in my under-Elder base. I created a room for them directly under the alter fire and sealed it up to the roof (floor of the alter).

Just after the eggs hatched, I got a bat raid. I had saved up all game for those eggs, and had about 200 coin to spare. I was so afraid that the bats would find some way to get in, but I ran out to lead the bats outside, dealt with them, and ran back in to check my chicks. They were fine!