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.
Combine hoisin, vinegar, soy sauce, ginger, oil, pepper, and garlic in a small bowl, stirring well with a whisk.
Combine peanuts, coleslaw, water chestnuts, and chicken in a medium bowl; toss well.
Spoon about 1/3 cup chicken salad in the center of each lettuce leaf; top each with 2 teaspoons sauce. Roll up; secure with a wooden pick.