In a large pot or Dutch oven, heat 1 tablespoon of olive oil over medium heat. Add the diced green bell pepper, small onion, celery, and minced garlic. Sauté for about 5 minutes, or until the vegetables are tender and fragrant.
Add the cubed chicken breasts and sliced andouille sausage to the pot. Cook for another 5-7 minutes, stirring frequently, until the chicken is browned and cooked through.
Stir in the tablespoon of tomato paste, mixing well with the meat and vegetables. Then, add the Cajun seasoning and the bay leaf, ensuring everything is evenly coated.
Add the long-grain white rice to the pot, followed by the chicken broth and undrained diced tomatoes. Stir everything together, making sure the rice is submerged in the liquid.
Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 20-25 minutes, or until the rice is tender and has absorbed the liquid. Stir occasionally to prevent sticking.
Once the rice is cooked, remove the bay leaf. Fluff the jambalaya with a fork and serve hot. Enjoy this delightful dish with your favorite sides or on its own!