In a large mixing bowl, combine the shredded rotisserie chicken, halved grapes, diced avocado, chopped celery, and red onion.
In a separate small bowl, mix together the Greek yogurt, mayonnaise, Dijon mustard, lemon juice, salt, and pepper until smooth.
Pour the dressing over the chicken mixture and gently fold everything together until well combined.
If using, stir in the chopped parsley for added flavor and freshness.
Taste and adjust seasoning with more salt and pepper if needed.
Chill the salad in the refrigerator for at least 30 minutes before serving to allow the flavors to meld.
Serve the chicken salad on a bed of greens, in a sandwich, or in a wrap.