Place the cottage cheese and Greek yogurt in a small food processor or blender.
Process on high for 30 seconds or until the mixture is completely smooth and resembles a thick dressing.
Transfer the blended mixture to a large mixing bowl.
Whisk in the Dijon mustard, lemon juice, garlic powder, salt, and black pepper until fully integrated.
Add the shredded chicken, diced celery, and minced red onion to the bowl.
Fold the ingredients together with a spatula until the chicken is evenly coated with the dressing.
Stir in the chopped chives.
Refrigerate for at least 30 minutes before serving to allow flavors to develop.