Grill the chicken breast for 5-6 minutes on each side, then cut into small dice. Peel and core the apple, then dice. Chop the celery stalks. In a bowl, mix together diced cooked chicken, celery walnuts and apple. Toss well to combine. Set aside. In another bowl, combine mayonnaise, honey and lime juice. Season to taste with salt (optional) and ground black pepper. Mix well, then set aside. Drizzle the dressing over the chicken salad and toss to coat the mixture evely with dressing and serve immediately. If making ahead of time, place chicken mixture and salad dressing in a separate container.