Preheat the oven to 400°F (200°C).
Place the avocado halves skin-side down in a baking dish. Use a spoon to remove approximately one tablespoon of flesh from the center of each half to enlarge the cavity.
In a mixing bowl, combine the shredded chicken, Greek yogurt, lime juice, garlic powder, salt, and pepper. Stir until the chicken is evenly coated.
Divide the chicken mixture equally and spoon it into the avocado cavities, mounding the top slightly.
Top each stuffed avocado with an equal portion of shredded Monterey Jack cheese.
Bake for 10 minutes or until the cheese is melted and bubbling and the avocado is heated through.
Remove from the oven and garnish with fresh cilantro before serving immediately.