In a medium bowl, combine mango, sweet pepper, jalapeño, basil, lime juice, vinegar and sugar. Cover and chill for at least 2 hours and no longer than 24 hours. Let stand at room temperature for 30 minutes before serving. Makes 2-1/2 cups (10 to 12 servings).
When handling hot chile peppers, wear plastic gloves. If bare hands touch the peppers, wash your hands well with soap and water.