Prepare 24 coals. When they are hot, place 8 coals under the cast iron dutch oven to preheat.
When the cast iron dutch oven is hot, add the oil and sear the chicken, breast side down for 5 minutes.
Remove the chicken and add the potatoes to the dutch oven. Place the chicken on top of the potatoes in the center of the dutch oven. Insert a meat thermometer into the thickest part of the breast.
Place the lid on, and evenly distribute the remaining coals on the top of the closed dutch oven.
Rotate the dutch oven 90-degrees every 15 minutes. You may need to add additional coals after 45 minutes or so to keep the temperature consistent (if you add 4 coals to the bottom, double the number and add 8 to the top).
Cook for 60-90 minutes, or until the internal temperature of the chicken reaches 165F / 74C.