In a large bowl, combine the shredded chicken, chopped pickles, celery, and red onion.
In a small bowl, whisk together the mayonnaise, sour cream, Dijon mustard, and pickle brine until smooth.
Pour the dressing over the chicken mixture and stir until everything is evenly coated.
Fold in the fresh dill. Season with salt and pepper to taste. Remember that pickles and brine add salt, so go easy at first.
Cover and refrigerate for at least 30 minutes to let the flavors meld. Stir again before serving. Serve cold or at room temperature.