Heat 1 tablespoon oil in a Dutch oven over medium-high heat. Brown the chicken in batches, then transfer it to a plate.
Add the sausage and cook until browned at the edges. Transfer it to the plate with the chicken.
Build and Simmer:
Add the remaining oil, onion, bell pepper, and celery. Cook for 6 minutes, then stir in the garlic, Cajun seasoning, thyme, and pepper for 30 seconds.
Stir in the rice, tomatoes, stock, bay leaf, chicken, and sausage. Bring to a boil, then cover and reduce the heat to low.
Cook without lifting the lid for 22 to 25 minutes, until the rice is tender. Rest covered for 10 minutes, discard the bay leaf, fluff, and garnish with scallions.
Notes
Cajun seasoning blends vary in salt; taste after the rice cooks before adding more.
Keep the heat low during the covered simmer to prevent scorching.