Heat grill. In medium bowl, combine melon, lemonade concentrate, cilantro, chile and 1/4 teaspoon of the salt; mix well. Cover; refrigerate until serving time.
Sprinkle chicken with pepper and remaining 1/4 teaspoon salt. When ready to grill, place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 10 to 15 minutes for breasts or 8 to 12 minutes for thighs or until chicken is fork-tender and juices run clear, turning once. Serve chicken with melon salsa.