To flatten each chicken breast half, place, boned side up, between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/4 inch thick; remove wrap.
Place chicken in large resealable food storage plastic bag. Add salad dressing; seal bag and turn to coat. Refrigerate at least 2 hours to marinate, turning occasionally.
Heat grill. When ready to grill, remove chicken from marinade; reserve marinade. Place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 8 to 10 minutes or until chicken is fork-tender and juices run clear, turning once and brushing occasionally with reserved marinade. Discard any remaining marinade.
During last 1 to 2 minutes of cooking time, place Texas toast on grill; cook until toasted, turning once. Also, top each chicken breast half with cheese slice; cook until melted.
Spread each toast slice with 1 to 2 teaspoons pizza sauce. Top each with cheese-topped chicken and pepperoni slice. Drizzle each with remaining pizza sauce.