Heat olive oil in a large skillet over medium heat. Add minced garlic and ginger. Cook for 1–2 minutes until fragrant but not browned.
Add ground chicken. Break it apart with a wooden spatula and cook for 6–8 minutes until no longer pink and slightly browned.
Stir in soy sauce, hoisin sauce, and rice vinegar. Add chopped water chestnuts and cook for 2–3 more minutes.
Turn off heat. Stir in sliced green onions and sesame oil. Let it rest for 1 minute.
Spoon filling into individual lettuce leaves. Serve warm with optional dipping sauces like hoisin or chili garlic sauce.