Heat grill. In medium bowl, combine peaches, lime juice and brown sugar; mix well. Stir in bell pepper, green onions, chile pepper and dash of salt.
Place 1 chicken breast half between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound with flat side of meat mallet or rolling pin until about 1/4 inch thick; remove wrap. Repeat with remaining chicken breast halves.
When ready to grill, oil grill rack. Lightly sprinkle chicken with 1/8 teaspoon salt and pepper. Place chicken on oiled rack on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 6 to 10 minutes or until chicken is fork-tender and juices run clear, turning once. Serve with salsa.