Heat the oil in a large pot or Dutch oven set over medium-high heat. Cook the chicken thighs for a few minutes, turning as necessary until browned on all sides. Remove them from the pot and set aside. Reduce the heat to medium. Add the sausage to the pot and cook, stirring frequently, for a few minutes or until browned. Remove from the pot and set aside.
Add the onion, pepper, celery, and garlic to the pot and sauté for about 5 minutes, until tender. Add the rice and cook for a minute, stirring well. Add the cooked sausage, bay leaf, chili powder, thyme, salt and Tabasco.
Add the stock and diced tomatoes and stir everything together. Bring the mixture to a boil. Add the chicken thighs to the pot, meat side down, on top of the rice. Reduce the heat to low, cover, and simmer for about 15 minutes.
Remove the lid and stir the jambalaya, keeping the chicken pieces more or less on top. Replace the lid and cook for another 15-20 minutes, until the liquid is absorbed, the rice is tender and the chicken is cooked through. Remove the bay leaf and season with salt and pepper. Scatter the shrimp over the jambalaya, cover, and cook for 5-10 minutes, just until the shrimp are pink and opaque. Serve it while it's hot.