Whisk mayonnaise, chutney and lime juice in large bowl. Mix in chicken, walnuts, 2 tablespoons cilantro, celery and red bell pepper. (Chicken salad can be made 4 hours ahead. Cover and refrigerate.)
Place lettuce leaves on platter. Spoon 1 heaping tablespoonful chicken salad in center of each leaf. Sprinkle remaining 3 tablespoons of cilantro over and serve with lime wedges alongside.