Pronounced: chi-lay-key-lays.
A classic poor man's Mexican casserole. It's a Mexican lasagna of sorts, assembled by layering corn tortillas, cheese, chicken, and some type of sauce (often what we Americans would call enchilada sauce). Bake to perfection. Extraordinarily: simple, good, and bad for you.
As with any dish, there are many variations, but it isn't chilaquiles without tortillas, cheese, and sauce.