Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the shredded chicken, softened cream cheese, buffalo sauce, ranch dressing, 1/2 cup of cheddar cheese, and mozzarella cheese. Mix until smooth and well combined.
Spread the mixture evenly into a greased 9×9-inch baking dish.
Sprinkle the remaining 1/2 cup of cheddar cheese on top.
Bake for 20-25 minutes, or until the dip is hot and bubbly.
Remove from the oven and let cool slightly.
Garnish with chopped green onions or crumbled blue cheese, if desired.
Serve warm with tortilla chips, crackers, celery sticks, or carrot sticks.