Cook chicken breast until tender (boil, bake, or use rotisserie). Allow it to cool, then shred or dice into bite-sized pieces.
In a large mixing bowl, whisk together mayonnaise, Dijon mustard, and lemon juice until smooth.
Stir in chopped celery, red onion, and grapes.
Add the shredded chicken and nuts (if using). Mix until all ingredients are evenly coated.
Sprinkle with salt and black pepper. Adjust mayo or mustard if needed.
Cover and refrigerate for at least 30 minutes to let the flavors blend. Serve on croissants, sandwich bread, wraps, or over a fresh bed of lettuce.