In a large skillet, heat oil over medium heat.
Add ground chicken, carrots, green onions, water chestnuts, and garlic and stir fry together, breaking up chicken, until chicken is no longer pink.
Mix together remaining ingredients in a bowl or measuring cup.
Pour about half of the sauce over the chicken mixture and bring to a low boil to slightly thicken sauce and have it incorporate with the chicken. Taste and add more sauce to your liking.
Fill lettuce cups with chicken mixture and serve immediately.
The extra sauce can be used as a condiment to serve with the wraps if more sauce is needed.
If you can find a clean organic Hoisin sauce, feel free to also use that as a condiment.