Remove tomatillos from shell and wash with warm water. Place in a pot and cover with water, and bring to boil over medium-high heat. Remove from heat and strain all liquid.
Place tomatillos in blender with remaining ingredients except oil - do not add any liquid. Preheat a small pan over medium-high heat and add the oil and let it heat. Add the salsa and cook until salsa has a thick consistency or desired texture. Season to taste with salt and pepper. Place on the side until needed.
Heat 1/4 cup of the oil in a large nonstick skillet over medium heat. Crack the eggs two at the time into the pan and cook, to the desired doneness, 2 to 3 minutes for slightly runny sunny-side-up eggs.
Meanwhile, heat remaining oil in a large sauté pan until simmering. Add onion and saute for 1 minute, add tortilla chips and sauté for 30 seconds more, stirring often. Add tomatillo sauce, mix well and cook for 30 seconds more. Add grilled chicken, incorporate ingredients and cook for 1minute more. Divide chilaquiles among the plates. Top each plate with two eggs. Garnish with fresh sliced radish, sliced onion, fresh cheese, fresh cilantro leaves, beans, and guacamole.
This recipe and photo are courtesy of Chef Hugo Ortega of Hugo's.