In a large bowl, whisk together Greek yogurt, lemon juice, lemon zest, Dijon mustard, salt, black pepper, and cayenne until smooth.
Add the cooked chicken, diced celery, red onion, dill, parsley, and chives.
Fold gently until all ingredients are evenly coated with the dressing.
Taste and adjust seasoning with more salt or lemon juice if needed.
Cover the bowl and refrigerate for at least 30 minutes to allow flavors to meld.
Serve chilled or at room temperature. Enjoy on bread, in lettuce cups, or with crackers.