Heat gas or charcoal grill. In small bowl, mix curry powder, salt and oil. Rub mixture over chicken breasts.
Place chicken and onion slices on grill over medium heat. Cover grill; cook 12 to 16 minutes or until juice of chicken is clear when center of thickest part is cut (170°F), and onion slices are tender, turning once.
Meanwhile, in small bowl, mix chutney, mayonnaise and ground red pepper; blend well. Spread chutney-mayonnaise mixture on cut sides of rolls. Place 1/3 cup mixed greens on bottom half of each roll. Top each with chicken, onion slice and 4 pieces of cheese. Cover with top halves of rolls.