Preheat oven to 350 degrees. Season both sides of the chicken with the salt and pepper.
Heat the oil in a Dutch oven or large heavy pot over medium-high heat. When the oil is hot, add the chicken in batches and cook until golden brown, 3 to 4 minutes on the first side, and 1 to 2 minutes on the second side. Transfer to a plate.
Reduce the heat to medium and add the onions, celery, and bell peppers to the fat remaining in the pan and cook, sitrring , until soft, about 3 minutes. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Add the flour and cook, stirring constantly with a wooden spoon to make a light roux, 1 1/2 to 2 minutes. Stirring constantly, slowly stir in the stock. Add the Kitchen Bouquet and the chicken base and stir well. Return the chicken to the pot and bring the liquid to a boil. Remove from the heat and cover. Carefully transfer the pot to the oven and bake until the chicken is tender, about 30 minutes.
To serve, transfer the chicken to 4 large plates and spoon the rice along the side. Spoon the gravy over the chicken and the rice, as desired, and serve immediately.