Heat the oil in large sauté pan over medium heat. Add the onion and ginger and cook, stirring frequently, until soft, 4-5 minutes. Add the ground chicken and turn the heat up to high. Cook, breaking up the meat with a wooden spoon until partially cooked through, about 5 minutes. Add the garlic and cook 1 minute more. Add the Thai sauce to the meat mixture and cook for a few more minutes. Take off heat. Stir in the scallions, cilantro, mint and peanuts, shredded carrots. Taste and adjust seasoning if necessary. Spoon into lettuce cups and serve with a lime wedge.