Preheat oven to 350 degrees°F.
Season chicken with salt and pepper.
In a large heavy pot, preferably a Dutch oven, heat 1 tablespoon oil over medium-high heat.
Add the chicken pieces and sauté until browned, about 5 minutes. Remove from pot and cut into bite-size pieces. Set aside.
Heat the remaining 2 tablespoons of oil in the pan over medium-high heat.
Add the cooked sausage and cook until starting to brown, about 4 minutes.
Add all remaining ingredients, except for the shrimp and cooked chicken. Add 2 tsp of salt and 1 tsp black pepper. Stir to fully combine.
Cover and cook in the oven until the rice is nice and tender, about 1 hour.
Remove from oven and stir in the shrimp and cooked chicken. Return to the oven (covered) for 15 minutes. The shrimp should be nice and pink, if it doesn't look fully cooked, return to the oven for another 10 to 15 minutes.
Stir with a wooden spoon and garnish with fresh parsley, if desired. Serve at once with additional hot sauce.