Heat the vegetable oil in a large skillet over medium-high heat for 1 minute.
Add the ground chicken and cook for 5 minutes, breaking it apart with a spoon, until browned and cooked through to 165°F / 74°C.
Stir in the garlic and ginger and cook for 1 minute until fragrant.
Add the water chestnuts, soy sauce, hoisin sauce, and rice vinegar, then stir and cook for 2 minutes until the sauce coats the chicken.
Remove from heat, stir in the green onions, and spoon the filling into the lettuce leaves to serve.