Heat grill. In small bowl, combine all salsa ingredients; toss gently to combine.
Place 1 chicken breast half 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. Repeat with remaining chicken breast halves. Brush both sides of chicken with oil. Sprinkle one side with paprika and pepper.
When ready to grill, place chicken, seasoned side down, 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. Top chicken with cheese; cook an additional 30 to 60 seconds, or until cheese is melted. Serve with salsa.