Place peanuts in a small nonstick skillet over medium-high heat; cook 3 minutes or until lightly browned, shaking pan frequently. Remove pan from heat; set aside.
In a small bowl, combine hoisin, vinegar, soy sauce, ginger, oil, pepper and garlic in a small bowl, stirring well with a whisk.
In a medium bowl, mix 2 tablespoons peanuts, slaw, water chestnuts, and chicken; add sauce and toss well.
Spoon about ⅓ cup of chicken salad in the center of each lettuce leaf; Sprinkle each lettuce wrap with remaining 1 tablespoon peanuts. Serve immediately.
Notes
If you are preparing this recipe as GLUTEN FREE, just make sure you are using brands of hoisin sauce, soy sauce and water chestnuts that are known to be GF.