Heat 1 tablespoon oil in a stock pot (or a very large, deep sauté pan) over medium-high heat. Add the chicken and sausage and sauté for 5-7 minutes, stirring occasionally, until the chicken is cooked through and the sausage is lightly browned. Transfer to a clean plate and set aside.
Add the remaining 2 tablespoons oil to the stock pot. Add bell peppers, celery, onion and garlic. Sauté for 6 minutes, stirring occasionally, until the onions are softened.
Add the crushed tomatoes, stock, rice, seasoning, bay leaf, and stir to combine. Continue cooking until the mixture reaches a simmer. Then reduce heat to medium-low, cover and simmer for about 25-30 minutes, or until the rice is nearly cooked through, stirring every 5 minutes or so along the way so that the rice does not burn.
Stir in the chicken and sausage, and remove and discard the bay leaf.
Taste season the jambalaya with salt, pepper, and additional Cajun seasoning if needed. (I typically add about 2 teaspoons salt and 1/2 teaspoon pepper.) Remove from heat.