If using rotisserie chicken, remove skin and bones, then shred or dice the meat into bite-sized pieces.
In a large bowl, whisk together mayonnaise, pickle relish (or chopped pickles plus brine), mustard, and sweetener if using.
Add the chicken, celery, red onion, and fresh herbs to the bowl.
Stir until everything is evenly coated with the dressing.
Season with salt and pepper to taste.
Cover and refrigerate for at least 30 minutes to allow flavors to meld.
Before serving, give it a final stir and adjust seasoning if needed.