Heat a 12-inch cast iron skillet to medium high. Coat the bottom with cooking oil.
Salt and pepper the drumsticks. After the skillet is heated, add the chicken and brown well on all sides. No need to cool thoroughly. The chicken will finish cooking in the skillet later. When browned, remove and set aside.
Add onion, bell pepper and celery to the hot skillet. Add more oil if necessary. Cook for 10 minutes or until vegetables are soft.
Add sausage and cook until heated and the sausage starts to render fat.
Add rice to skillet and stir well. Cook uncovered, stirring frequently, until most of the juices are absorbed.
Add chicken stock and Cajun seasoning. Stir well.
Return chicken drumsticks, and its juices, to the skillet.
Cover, reduce heat to medium low and cook 15 minutes or until most of the cooking liquid is absorbed by the rice.
Remove from heat, keep covered and let sit for 10 minutes for the rice to completely absorb all the liquid.