Heat the oven to 325℉.
Place a large dutch oven over medium heat and add two tablespoons of the oil. When the oil is hot, add the chicken and brown. (It's best to do this in a single layer, which typically requires at least two batches.) Set the browned chicken aside. Fond will begin to develop on he bottom of the pot as you brown the meat, but don't let it scorch. (If it begins to look burned at any point, simply add a bit of liquid or adjust the heat down.)
Next add the Andouille sausage and brown. Set the browned sausage aside. At this point, the bottom of the pot should be thoroughly darkened and covered with fond. (Do not be alarmed...this is exactly what you want for building flavor.)
Add the remaining two tablespoons of oil to the pot. When it is hot, add the onion, celery, and green pepper for the trinity. Sauté this mixture for about 10 minutes, stirring occasionally. Then add the garlic and cook for another minute or two.
Add the drained tomatoes, mixture of tomato juice and chicken stock, and hot sauce. Toss in the bay leaves and bring the mixture to a boil.
Add the rice and stir.
Add the browned chicken and sausage. Give the whole mixture another good stir and bring the pot back to a simmer.
Cover the pot with a lid and transfer it to the oven. Cook for about 40 to 45 minutes, or until the rice is tender and has absorbed all the liquid.
Serve the jambalaya with more hot sauce alongside. If you want to garnish the dish, scatter some chopped fresh leaf parsley or scallions over the top. Discard the bay leaves as you find them.