Heat oil in a large skillet over medium-high heat.
Add ground chicken and cook until browned and cooked through, breaking it up with a spoon as it cooks, about 6-8 minutes.
Add diced bell pepper and water chestnuts to the skillet and sauté for 2 minutes until peppers are slightly tender.
Add minced garlic and cook for another 30 seconds until fragrant.
In a small bowl, whisk together hoisin sauce, soy sauce, rice vinegar, and sesame oil.
Pour the sauce mixture into the skillet and stir to coat all ingredients evenly. Cook for 1-2 minutes until heated through.
Remove from heat and let cool slightly.
Serve the chicken mixture in lettuce leaves, garnished with green onions and chopped peanuts.