Shred the cooked chicken into bite-size pieces. For best flavor, use a combination of white and dark meat.
In a large bowl, combine mayonnaise, Dijon mustard, chopped sweet pickles, and diced celery. Stir until well mixed and creamy.
Add the shredded chicken and chopped boiled eggs to the bowl with the dressing mixture.
Season with salt and freshly ground black pepper, then toss gently to coat everything evenly. Be careful not to overmix.
If using optional ingredients like red onion, grapes, herbs, or nuts, fold them in gently at this stage.
Taste and adjust seasonings as needed.
Cover and refrigerate for at least 30 minutes before serving to allow flavors to develop. For best results, chill for 2 hours.
Serve on bread for sandwiches, over lettuce, with crackers, or in lettuce cups.