Preheat the oven to 350°.

Heat the oil in a Lodge 12-inch cast iron skillet over medium-high heat until shimmering. Season the chicken with salt and pepper on both sides, and add to the hot oil. Cook until browned on both sides, 3 to 5 minutes total.

Remove to a plate.

Pour off any rendered fat in the skillet, and discard. Add the andouille and cook, stirring occasionally, until the meat starts to brown and render fat, about 3 minutes. Add the Cajun seasoning and stir to combine. Add the onion, celery, and bell pepper; cook, stirring occasionally, until the vegetables start to color, 5 to 7 minutes. Add the garlic and cook until fragrant, 45 to 60 seconds. Add the rice and stir to coat. Stir in the tomato sauce and stock and bring to a boil. Return the seared chicken thighs to the skillet and nestle them, without crowding, into the rice. Tuck the bay leaf into the rice. Transfer to the oven and bake, uncovered, for 30 minutes.

Add the shrimp and stir to combine. Continue to bake, uncovered, until the rice is tender, the shrimp are opaque, and the juices of the chicken run clear when pierced with the tip of a knife, signifying the chicken is done, about 10 minutes. Remove the skillet from the oven to a wire rack to cool slightly.

Taste and adjust the seasoning with salt and pepper. Remove bay leaf before serving. Spoon the jambalaya into warm serving bowls. Serve immediately.