In a large bowl, combine the ground chicken with the coconut milk, carrot, chiles, basil, fish sauce, sugar, lime juice, garlic, egg, shallot, ginger, salt and pepper. Using your hands, mix thoroughly.
Hold a wonton wrapper in the palm of your hand; keep the rest covered with plastic wrap. Place a rounded tablespoon of filling in the center of the wrapper and pinch the edges all around to form a cup that is open about 1 inch at the top. Keep the shumai covered with plastic wrap. Repeat with the remaining wonton wrappers and filling.
Fill a wok or a very large skillet with 2 inches of water and bring to a boil. Line a double-tiered bamboo steamer with lettuce leaves and arrange the shumai in the steamer without crowding. Cover and steam over moderate heat until cooked through, about 10 minutes. Repeat with the remaining shumai. Serve right away, passing the chili sauce at the table.