Cut into the fat, rounded side of each chicken breast to butterfly them open. Place chicken in baggies or between plastic and gently pound them into very thin, large cutlets. Season with salt and pepper on each side.
Combine breadcrumbs with tortilla chip crumbs. Line up three dishes to dredge cutlets; one with flour, one with the egg and one with the tortilla chip breadcrumbs.
Preheat oven to 200°F and place a metal rack on a baking sheet to keep cutlets warm while preparing them in batches.
Heat a shallow layer of oil (1/8- to 1/4-inch) in a very large skillet over medium to medium-high heat.
Coat chicken cutlets in flour and shake off excess, drop them in the egg and drain excess and then coat them evenly in the breadcrumb mixture. Shallow fry the cutlets 1 or 2 at a time for 3 minutes on each side. Keep finished cutlets warm in oven as you finish the rest.
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