1. Preheat oven to 400°. Sprinkle chicken with 2 tsp. salt, pepper, and paprika.
2. Heat oil in a 12-inch cast-iron skillet over high heat until oil just begins to smoke.
3. Place chicken in skillet, skin sides down; reduce heat to medium-high, and cook 15 minutes. Transfer chicken to a plate; discard drippings.
4. Place potatoes in a single layer in skillet, and sprinkle with 1 Tbsp. chopped fresh rosemary and 1/4 tsp. salt. Place chicken, skin sides up, in skillet, and sprinkle with 1/4 tsp. chopped fresh rosemary.
5. Bake at 400° for 25 to 30 minutes.