In a large skillet set over medium heat, heat olive oil. Sauce the onion and cook for about 3 minutes then add the mushrooms and cook an additional 3 minutes. Add garlic and cook just until fragrant, about 30 seconds, stirring constantly.
Add ground the ground chicken and cook until browned, making sure to break up any large chunks.
In a small bowl, combine the coconut aminos, sesame oil, rice wine vinegar, ginger, and hot sauce. Whisk until smooth then pour over meat mixture. Stir until combined. Add the chestnuts and green onions. Cook for 3-4 minutes then remove from the heat. Season with salt and pepper to taste.
Make sauce: whisk together all sauce ingredients in a small bowl.
Spoon a few tablespoons of the meat mixture into the center of a lettuce leaf and serve with the sauce. Garnish with green onions, if desired.
