In a large skillet, heat the vegetable oil over medium heat. Add the chopped onion and sauté for about 3 minutes until softened.
Add the minced garlic and cook for an additional 30 seconds until fragrant.
Increase the heat to medium-high and add the ground chicken. Cook until browned and fully cooked, breaking it apart with a spatula, about 5-7 minutes.
Stir in the diced water chestnuts, soy sauce, hoisin sauce, rice vinegar, sesame oil, ground ginger, and black pepper. Cook for another 2-3 minutes, allowing the flavors to meld.
Remove the skillet from heat and let the mixture cool slightly.
To serve, spoon the chicken mixture into the lettuce leaves, garnish with sliced green onions and sesame seeds, and wrap them up like tacos.