Roasting the chickens and using both dark and white meat results in chicken salad with deep flavor. (Buying rotisserie chickens will cut down on the timing, but be sure to choose minimally seasoned birds.) Fennel, standing in for the usual celery, along with fennel seed and fresh basil, adds an unexpected note of sophistication.
Cooks' note:
Chicken salad, without basil, can be made 1 day ahead and chilled, covered. Stir in basil before serving.