In a small bowl, whisk together the ingredients for the sauce (sesame oil, rice vinegar, soy sauce, garlic, ginger, honey, peanut butter, coconut milk, Sriracha, and cornstarch). Whisk until evenly combined (some small lumps of peanut butter may remain).
Heat a large wok or sauté pan over high heat. When the pan is hot, add the oil (it should shimmer). Carefully add the chicken to the pan and cook, stirring continuously until the chicken begins to brown on the outside, 3-4 minutes. Add the prepared sauce to the pan all at once. Cook, stirring continuously, until the sauce has thickened slightly and the chicken is cooked through, about 2 minutes.
Transfer the chicken to a serving dish. Serve immediately with the lettuce leaves, peanuts, chilis, and lime wedges on the side. Spoon about 1/4 cup of chicken mixture, peanuts, and chilis on top of each lettuce leaf and squeeze a lime wedge over the top just before eating.