Pre-heat 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 saute 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 sausage and cook until starting to brown, about 4 to 5 minutes.
Add the onion, bell pepper, celery, jalapeño and garlic. Sauté until soft, about 5 minutes.
Add the tomato paste, vinegar and hot sauce and stir to combine, about 1 minute.
Add the thyme, cayenne, garlic powder, chili powder, and a healthy pinch of salt and pepper. Cook until aromatic, about 2 minutes.
Stir in the tomatoes, reserved tomato liquid, stock, bay leaves, and then rice.
Cover and cook in the oven until the rice is nice and tender, about 1 hour.
Remove from the oven and test the rice. If still a little stiff, place back in the oven for another 15 to 20 minutes. Then, remove from oven and stir in the shrimp and cooked chicken.
Return to the oven (covered) for 5 minutes. Remove from oven and let stand for 15 minutes.
Stir with a wooden spoon and then plate into warmed bowls and serve at once.
Serve with additional hot sauce.