Cut four sides lengthwise from red pepper, leaving stem ends and seeds intact. Discard stem and seeds. Combine chili powder, salt, and 1/4 teaspoon black pepper; sprinkle evenly over chicken and pepper quarters.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place chicken and pepper quarters on rack; grill, covered, 4 to 5 minutes on each side or until chicken is done and pepper is tender. Cool slightly; slice chicken and pepper quarters into strips.
Combine chicken and pepper strips, beans, and next 3 ingredients in a large bowl; toss well. Cover and chill 10 minutes or until ready to serve. To serve, place 1 cup lettuce on each of 4 individual serving plates. Arrange chicken mixture evenly over lettuce, and sprinkle each serving with 2 tablespoons cheese. Arrange 6 tortilla chips on each salad plate.