Heat the vegetable oil in a Dutch oven over medium heat; cook and stir the onions, bell pepper, salt, and cayenne pepper until the vegetables are a deep brown color, about 20 minutes. Add the andouille sausage, and continue to cook, stirring often, for 10 to 15 minutes. Drain any fat. Stir in the chicken and bay leaves; cook and stir until the chicken is browned, about 8 minutes.
Stir in the rice, and cook for 2 minutes. Pour in water; cover and cook over medium heat, without stirring, until the rice is tender and the liquid has been absorbed, about 30 minutes. Remove the bay leaves, stir in the green onions and serve.
