In medium saucepan, sauté bacon over medium-low heat until just crisp. Add onion; cook until light browned, about 7 minutes. Stir in tomatoes and green chilies; cook for 3 minutes more. Sprinkle salt and pepper into dish; stir. Remove from heat, cover and set aside.
Between two sheets of plastic wrap, place chicken breasts. Pound with meat hammer to 1/4 inch thickness.
Place four in pie plate or other flat dish. Place egg white in shallow bowl. Place tortilla chip crumbs in third bowl. Dip each chicken breast first into flour, patting off excess, then into egg. Finish by coating with crumbs.
In large, non-stick skillet, warm oil over high heat. Add chicken and brown each side, turning after about 3 minutes. Reduce heat to medium-low; continue to cook chicken until firm, about 5 more minutes on each side.
To serve, place chicken on platter. Warm relish and spoon on top of chicken.