In a large mixing bowl, whisk together the Greek yogurt, Dijon mustard, and lemon juice until the consistency is smooth.
Add the shredded rotisserie chicken, diced celery, minced red onion, and halved grapes to the yogurt mixture.
Using a large spoon or spatula, fold the ingredients together until the chicken and vegetables are evenly coated with the dressing.
Season with salt and black pepper, then stir in the chopped fresh parsley.
Cover the bowl and refrigerate for at least 20 minutes to allow the flavors to meld.
Serve chilled over a bed of greens, inside whole-grain wraps, or in lettuce cups.