Grill the chicken. Rub chicken on all sides with olive oil, and zest and juice of the lime. Season generously with salt. Grill on an outdoor grill or in a grill pan until cooked through, about 15 minutes total. Thinly slice and cover with foil until ready to serve.

Heat the oil. Heat the 2 cups of oil in a large (14-inch) frying pan over medium-high heat. If you don't have a frying pan this big use a Dutch oven. Check to see if the oil is hot enough by testing with a wooden chopstick. The oil is hot enough when it is immediatly covered with bubbles.

Fry the tortillas. Add tortilla wedges a handful at a time—don't crowd the pan—and fry until crisp and golden on both sides, about 2-3 minutes total. Remove to a paper towel-lined plate and sprinkle with salt. Repeat with remaining tortillas.

Heat the sauce. Pour off all but 1/4 cup of the oil into a heatproof bowl. Return the pan to medium-high heat. Carefully add the sauce, stirring as you pour it in, and fry for a few mintues in the oil.

Add the chips and chicken. Add the tortilla chips and chicken and stir to coat in the sauce.

Garnish and serve! Divide the chilaquiles between 4 plates and serve letting everyone garnish at the table or you can garnish each plate with the sour cream, sliced avocado, queso fresco, and Cotija cheese.