Finely chop the dill pickles, celery, and red onion. Place them in a large mixing bowl along with the shredded or diced cooked chicken. Add the fresh dill and give everything a quick toss to distribute.
In a small bowl, whisk together the mayonnaise, pickle juice, Dijon mustard, salt, and pepper until smooth. Taste and adjust seasoning if needed — you can add a pinch more salt or extra pickle juice for more tang.
Pour the dressing over the chicken mixture and fold gently until everything is evenly coated. Cover the bowl and refrigerate for at least 20 minutes (or up to overnight) to let the flavors meld.
Spoon the chilled chicken salad onto your choice of serving vehicle — toasted sourdough, croissants, butter lettuce leaves, or simply with crackers. Garnish with extra fresh dill and a few thin pickle slices if desired.