My favorite place for a chicken coop is under the Elder shrine and using that eternal fire as the warmth for the chickens. Since they are below the fire and cannot possibly get to it they are pretty much safe. Also the walls are earthen walls, all sealed nice and tight with only a portal in and out.

I did at first have troubles with chickens and so forth, eggs showing up beyond the pen walls i would build and them darn bastards that just seem to straight line it to the fire. Even when it was outside the pen, but perhaps too close. Anyway the move to the Elder shrine was a good move for me. Happy to report, not a single chicken lost since then, and I have a healthy amount of eggs, chicken meats, and tons of clucking cluckers just eating me out of barely. XD