Preheat your oven to 350°F (175°C). If using a skillet, ensure it's oven-safe. If using a baking dish, lightly grease it.
In a medium mixing bowl, combine the softened cream cheese, ranch or blue cheese dressing, and hot sauce. Stir until smooth and well combined. This forms the creamy base of your dip.
Add the shredded cooked chicken to the cream cheese mixture. Stir until the chicken is evenly coated.
Fold in the shredded cheddar cheese and Monterey Jack cheese. If you're using blue cheese, gently fold it in now as well.
Transfer the mixture to your prepared oven-safe skillet or baking dish, spreading it evenly.
Bake for 20-25 minutes, or until the dip is hot, bubbly, and the cheese is melted and slightly golden.
Remove from the oven and let it sit for a few minutes before serving. Garnish with fresh chives or green onions.