Chop or shred the cooked chicken into bite-sized pieces and place it in a large mixing bowl.
Mix in diced celery, red onion, grapes, nuts (if using), and parsley.
In a small bowl, whisk together mayonnaise, Dijon mustard (if using), lemon juice, salt, and pepper.
Pour the dressing over the chicken mixture. Gently toss until everything is well coated. Taste and adjust seasoning if needed.
Cover and refrigerate for at least 30 minutes to allow the flavors to meld. Serve chilled on a bed of lettuce, with crackers, or in a sandwich or wrap.