Prepare Chicken: Remove skin from the rotisserie chicken and shred 3 cups of meat using a fork or your hands. Add to a large bowl.
Chop the Add-Ins: Finely dice celery, onion, and grapes (if using). Add to the bowl with the chicken.
Mix the Dressing: In a small bowl, whisk together mayonnaise, Dijon mustard, lemon juice, salt, and pepper until smooth.
Combine Everything: Pour the dressing over the chicken mixture. Add nuts if using. Stir gently until everything is evenly coated.
Chill (Optional): For best flavor, cover and refrigerate for at least 30 minutes before serving.
Serve and Enjoy: Serve on a sandwich, in lettuce wraps, over a green salad, or with crackers.