On each level of the Dungeons of Doom past level 16, there is a 1/8 chance of a cockatrice nest existing on the level (provided cockatrices have not been genocided or made extinct). The nest is simply a large room filled with sleeping cockatrices and statues of their unfortunate victims. Cockatrice nests do not generate any ambient messages, so be careful and use your telepathy early and often.

In my experience it is unwise to invade a cockatrice nest unless you can do so very quietly. If you accidentally wake the cockatrices, you'll have some problems, because although the chances of being petrified while fighting a cockatrice are fairly small, the overall chance of being petrified gets much higher if you're fighting twenty of them. Don't invade a cockatrice nest when there's a new moon. Just don't.