Heat the vegetable oil in a large skillet over medium-high heat. Add the ground chicken in an even layer and let it cook undisturbed for 1-2 minutes before breaking it up.
Continue cooking, breaking the chicken into smaller pieces, until mostly cooked through, about 4-5 minutes.
Add the garlic and ginger and cook for 1 minute, until fragrant.
Stir in the water chestnuts, hoisin sauce, soy sauce, rice vinegar, and sesame oil. Cook for 2-3 minutes, until heated through and the chicken is fully cooked.
Remove from heat and stir in the sliced green onions.
Spoon the chicken mixture into lettuce leaves and top with sesame seeds or chopped peanuts, if using.