Heat 1 tablespoon oil in a Dutch oven 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.
Add the remaining 2 tablespoons of oil to the pot. Add bell peppers, celery, serrrano, onion, and garlic. Sauté for 6 minutes, stirring occasionally, until the onions are softened.
Add the crushed tomatoes, chicken stock, rice, Cajun seasoning thyme, cayenne, 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 so the rice does not burn.
Stir in the chicken and sausage, and remove and discard the bay leaf. Taste and season the jambalaya with salt, pepper, and additional Cajun seasoning if needed. Remove from heat. Serve with desired garnishes.