If using raw chicken, cook 2 large chicken breasts (boiled, grilled, or baked) until internal temperature reaches 165°F (75°C). Shred using forks or a hand mixer.
In a large bowl, combine mayonnaise, Greek yogurt, Dijon mustard, lemon juice, salt, and black pepper. Whisk until smooth.
Add shredded chicken, celery, red onion, grapes, almonds, and parsley to the bowl. Gently fold everything together until evenly coated.
Refrigerate for at least 30 minutes before serving to allow flavors to meld.
Serve on croissants, bread, lettuce wraps, or with crackers.