1. To prepare the jambalaya, in a large bowl, combine the oil, chicken and enough jerk seasoning to coat the chicken and toss.
2. Heat a large pot or Dutch oven over medium-high heat. Add the seasoned chicken, reduce the heat to medium and sear the chicken so each piece is evenly browned on all sides, about 5 minutes. If the chicken is sticking, add a touch of oil to the pot. Transfer the chicken to a plate.
3. Keep the pot over medium heat and add the andouille sausage. Cook, stirring, for a few moments, then add the onion and bell peppers plus more oil if the vegetables begin to stick. Cook, stirring occasionally until the vegetables begin to soften. Add the celery and cook, stirring occasionally, for 1 minute. Add the garlic and cook, stirring occasionally, until aromatic.
4. Add the rice and stir to blend with the other ingredients. Cook, stirring occasionally, for about 3 minutes. You do not want any color on the rice, but if some grains are beginning to turn golden brown, just proceed to the next step.
5. Add 1 tablespoon of the jerk seasoning and cook for a few moments, stirring constantly. Return the chicken to the pot.
6. Add the tomatoes with juices and the stock; the liquid should be covering the rice by about 1 inch. Taste the liquid and adjust for seasoning. You do not want the liquid to taste bland and flavorless, but you also do not want the seasoning to be too bold. Instead, you want to taste a hint of each flavor and a nice balance between the stock and the seasoning.
7. Bring the liquid to a boil, reduce the heat to low, cover and simmer until the liquid has been absorbed and the rice is tender about 20 minutes. Remove from the heat and fluff with a fork. Let cool for a few minutes, then serve.