• Warm the olive oil in a heavy 5-quart Dutch oven or large pot set over medium-high heat. Lightly season the chicken pieces with a sprinkle of Cajun seasoning and brown them for 3–5 minutes, stirring occasionally. The chicken should take on color but remain slightly undercooked. Remove from the pot and set aside.
• Add the sliced sausage to the same pot, allowing it to brown for about 5 minutes. Once it releases some flavorful oil and turns golden, stir in the onion, bell pepper, and celery mixture. Use a wooden spoon to scrape up the flavorful browned bits at the bottom of the pan. Cover and cook over medium heat for 5 minutes, stirring once midway through.
• Return the browned chicken to the pot. Add the canned tomatoes, chicken broth, and all the listed herbs and spices. Stir thoroughly, taste the liquid, and adjust the seasoning if necessary.
• Pour in the uncooked rice and mix until well distributed. Bring the mixture to a gentle boil, then cover and reduce the heat to the lowest simmer. Cook for 10 minutes, then stir once to bring some of the rice from the bottom to the top.
• Cover again and let the jambalaya cook slowly for another 30 minutes, or until the rice is tender and has absorbed the rich, flavorful broth. Avoid lifting the lid during this time, as the steam is essential for proper cooking. Maintain a gentle simmer rather than a boil to prevent sticking or burning.
• If the rice remains slightly firm after 30 minutes, pour in about ½ cup of additional broth, stir gently, and continue cooking for 5–10 more minutes.

Alternative Oven Method:

• After browning the chicken and sausage on the stovetop, combine them with the tomatoes, broth, rice, and seasonings in the same pot. Bring the mixture to a brief boil, then transfer it to a heavy-duty roasting pan (approximately 11¾ x 9¼ x 2½ inches). Seal the pan tightly with heavy-duty aluminum foil or a fitted lid to lock in steam. Bake in a preheated oven at 350°F (175°C) for 1 hour, or until the rice is tender and perfectly cooked.