Preheat the oven to 400 degrees F.
Put the chips in a food processor and pulse until they are finely ground; set aside.
Slice the chicken breasts in half horizontally so you have 4 thin chicken cutlets.
Set up a breading station with 3 shallow dishes: Stir together the flour, chili powder and 1/2 teaspoon salt in the first dish. Beat the eggs in the second dish and add the tortilla chips to the third dish. Coat a cutlet in the flour. Dip in the egg, letting any excess drip off and then press into the tortilla chips. Transfer to a plate and bread the remaining cutlets.
Heat 1/4 cup of the oil in a large nonstick skillet over medium heat until a piece of the breading sizzles when added to the oil. Add 2 breaded cutlets to the oil, making sure they don't touch each other. Fry until golden brown on both sides, 3 to 4 minutes per side. Remove to a paper towel-lined plate. Add the remaining 1/4 cup oil to the skillet, heat and then fry the remaining cutlets.
Evenly spread 1/2 cup salsa on the bottom of a 9-by-13-inch baking dish. Arrange the chicken in a single layer on top. Pour 1/4 cup of salsa on top of each piece of chicken. Shingle the cheese evenly over the chicken.
Bake until the cheese is bubbling and golden brown, 25 to 30 minutes.
Sprinkle with the jalapeno and cilantro.
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