In a large nonstick skillet set over medium heat, add the oil. When the oil is hot, add the chicken and cook throughout.
Add celery, chestnuts, mushrooms and garlic, cook until tender, about 4 minutes.
Add ginger, soy sauce, sesame oil, oyster sauce and chili paste, mix to combine. Cook for an additional 3-4 minutes. Remove from the heat.
Scoop warm mixture into the lettuce leaves, top with carrot, cashews and green onion. Serve immediately.