Heat your pot or Dutch oven over medium heat. Add the sliced Andouille sausage and cook until browned. Remove and set aside.
In the same pot, add the diced chicken and cook until it's no longer pink. Remove and set aside.
In the same pot, add the onion, green pepper, and celery. Sauté until they become tender and fragrant, about 5 minutes.
Add minced garlic and continue cooking for another minute.
Add the diced tomatoes, rice, chicken broth, bay leaf, Cajun seasoning, thyme, salt, and pepper. Mix well.
Put back the cooked sausage and chicken in the pot. Stir everything together.
Bring the mixture to a boil, after that reduce the heat to low, cover, and let it simmer for about 20-25 minutes, or until the rice is tender and the liquid is absorbed.
Once cooked, remove the bay leaf and fluff the Jambalaya with a fork.