Mix together basil, orange juice, vinegar, garlic, 1/2 teaspoon salt, 1/4 teaspoon pepper and tomatoes in small bowl. Refrigerate for at least 1 hour.
Preheat broiler with pan 4 inches from heat, or prepare grill with hot coals with rack 4 inches from coals.
Rub chicken breasts with olive oil and the remaining salt and pepper.
Broil or grill chicken, turning frequently, for 6 to 7 minutes per side or until no longer pink in center.
Serve each breast topped with some of the relish.