Chilaquiles is a sort of top-of-the-stove tortilla casserole. In its simplest form, it consists of a freshly made salsa into which you stir fried tortillas. Sometimes eggs are added, and sometimes chicken as well. The salsa can be red or green; even thick black beans may be used.
Combine the tomatoes, chiles, chopped onion and garlic in a blender, and blend until coarsely pureed.
Heat the oil in a large, heavy nonstick skillet or a wide saucepan over medium-high heat, and add a drop of the puree. It should sizzle. Add all of the tomato puree, and cook, stirring, for about 5 to 10 minutes, until the sauce darkens, thickens and begins to stick to the pan. Add water or stock if the mixture seems dry, and season to taste with salt. Turn the heat to low, and simmer, stirring often, for about 15 minutes, until the sauce coats the front and back of a spoon. Taste and adjust salt.
Stir in the chicken and heat through. Stir in the tortilla chips or pieces, stir together for a half minute, and remove from the heat. Spinkle the cheese, cilantro and sliced onion over the top, and serve.
The poached, shredded chicken breast will keep for three days in the refrigerator. You can make this dish ahead through step 2 and remove from the heat. Reheat gently and proceed with step 3, then serve right away.