Preheat oven to 350 degrees. Season chicken on skin side with 1/2 tsp each salt, pepper, and paprika. Heat 1 tbsp olive oil over medium in a 12 inch cast iron skillet. Add chicken, skin side down, and cook for 3 minutes or until golden brown. Flip and cook an additional 3 minutes. Remove chicken and set aside.
Add peppers, onions, and chorizo to the pan. Cook for 4-5 minutes or until onions are translucent.
Add saffron, the remaining 1 tsp smoked paprika, 3/4 tsp kosher salt, and rice and cook for 1 minute. Add chicken broth and white wine or water. Nestle chicken into the rice, skin side up.
Cover with an oven-safe lid or tin foil and bake 35 minutes. Uncover and bake for an additional 10 minutes. Turn oven to broil and cook for a final 2-3 minutes to crisp the chicken skin again. Keep a close eye on it during broiling so it doesn't burn!