Start by removing all the meat from the rotisserie chicken. Discard any skin or bones, unless you prefer to keep them for other recipes like chicken stock. Shred the chicken into bite-sized pieces, ensuring you have about three cups.
Wash and chop the celery stalks into small, crunchable pieces. Dice the red onion finely or slice it thinly, depending on your preference. Properly chopped veggies give the salad a balanced crunch in every bite.
Add the shredded chicken, celery, and red onion to a large mixing bowl. Incorporate the mayonnaise and brown mustard, stirring everything together until well-coated. The dressing binds all the ingredients and brings out their flavors.
Add salt and pepper to taste. Stir well to ensure even seasoning. Taste as you go and adjust depending on your preferences.
Transfer the chicken salad to an airtight container and refrigerate for at least 30 minutes before serving. Chilling allows the flavors to meld beautifully together. Serve directly or store for later; it’s even better the next day!