Preheat your oven to 375°F (190°C).
In a medium mixing bowl, combine the shredded cooked chicken breast, Greek yogurt, Neufchatel cheese, buffalo hot sauce, garlic powder, and onion powder.
Stir the mixture vigorously until the chicken is fully coated and the ingredients form a uniform, creamy base.
Transfer the mixture into a small oven-safe ramekin or baking dish, smoothing the top with a spatula.
Evenly sprinkle the shredded mozzarella cheese over the top of the chicken mixture.
Place the dish in the oven and bake for 15 to 20 minutes, or until the dip is heated through and the cheese is melted and golden brown.
While the dip bakes, slice the celery and carrots into sticks for dipping.
Remove the dish from the oven, garnish with finely chopped fresh chives, and serve immediately alongside the fresh vegetable sticks.