Add the shredded rotisserie chicken, quartered red grapes, small diced Fuji apple, small diced celery, and minced shallots to a large mixing bowl.
In a small mixing bowl combine the mayonnaise, lemon juice, minced fresh parsley, minced fresh chives, and Dijon mustard.
Whisk the mayonnaise mixture until smooth and evenly combined.
Pour the mayonnaise mixture over the chicken mixture.
Gently fold the dressing into the chicken mixture until all ingredients are evenly coated.
Taste and season with kosher salt and black pepper, adding a little at a time and mixing after each addition until the seasoning is to your liking.
Cover and refrigerate if not serving immediately. Serve plain, on bread, in a wrap, or on lettuce wraps.