The high heat of a grill means that pounded chicken breasts (paillards) cook in a flash and don't have time to dry out. You can buy thin cutlets, which are pricier, or flatten the chicken yourself, as we do here. A mint salad rounds out the meal.
Slice each chicken breast almost in half horizontally, leaving one side attached. Open like a book. Place each breast between sheets of plastic wrap and pound to about 1/4 inch thick with a meat mallet or small skillet. Heat a grill pan or grill to high; clean and lightly oil hot grill. Season chicken with salt and pepper and grill until cooked through, about 3 minutes per side. Slice chicken breasts in half, divide among four plates, and drizzle with 2 tablespoons dressing.
In a large bowl, toss together lettuce, mint, carrot, onion, and 3 tablespoons dressing; serve over chicken.