In a medium bowl, stirring with spoon, combine the chile, garlic, sugar, vinegar, lime juice, fish sauce, oil, onion, and black pepper, set aside for 1/2 hour. In a large bowl combine cabbage, carrot, chicken breast, and mint, tossing with tongs. Pour cabbage mixture over the dressing, tossing with tongs, slowly and patiently so everything is coated. Add salt, to taste. Serve on a flat plate with mint for garnish.