In a medium bowl, whisk together 1 cup mayonnaise, 2 tablespoons fresh lemon juice, 1 tablespoon chopped fresh parsley, 1 teaspoon kosher salt, and 1/2 teaspoon fresh ground pepper until smooth and creamy.
In a separate large bowl, combine 4 cups cooked diced chicken, 1 cup halved or quartered seedless red grapes, 1 cup chopped red apple, 1 cup chopped celery ribs, and 1 cup chopped or sliced nuts.
Pour the dressing over the chicken mixture and stir gently until everything is evenly coated.
Cover and chill for at least 1 hour to let flavors meld.
Serve on bread or croissants, in lettuce cups, pita bread, or with crackers.