Preheat the oven to 350 degrees F (175 degrees C). Prick potatoes several times with a fork and place onto a baking sheet.

Bake in the preheated oven until potatoes are easily pierced with a fork, 1 1/2 to 2 hours. Check for doneness after 1 hour and then every 15 minutes until reached desired doneness.

While potatoes bake, heat oil in a large skillet over medium heat. Add chicken; cook and stir until chicken is no longer pink in the center and juices run clear, about 5 minutes.

Cut potatoes in half horizontally; scoop out potato flesh into a large bowl and set skins aside. Stir in butter until melted and combined; season with salt and black pepper. Stir in chicken, 2 cups Cheddar cheese and Buffalo sauce until combined. Spoon potato filling back into empty skins. Sprinkle remaining 1 cup Cheddar cheese on top.

Bake in the preheated oven until filling is hot and cheese melted, about 20 minutes.