In a small bowl make a marinade by combining and whisking oil, and the seasonings. Coat the chicken pieces evenly with a marinade, and let rest between 5-30 minutes. (If it's hot out leave it in the fridge.) Heat oven to 480°F/ 250°C. Grease the pan with oil and place the drumsticks and thighs in. Also, add the remaining marinade. Bake for 15 minutes.
Take the pan out, and flip the chicken pieces around. Return the pan to the oven. Lower heat to 360°F/ 180°C and bake for another 15 minutes. At this point, take the chicken pieces out of the pan and set them aside. Carefully scrub any chicken parts and grease remaining in the pan after baking, and leave them inside the pan.
Add rice, and 4.5 cups of water (or chicken broth). Stir it around so it's evenly distributed. Bring the heat up to 400-420°F/ 200°-210°C again, and bake the rice for 25 minutes. At, or near the end, (when there is a quarter of an inch of water left in the pan above rice), turn off the heat and add chicken into the pan. Leave in the oven for a few minutes to absorb the extra moisture, then serve. (If you like your rice drier, keep it in a little longer.)
Serving: serve warm, with homemade bread and a side salad. Storing: Warning - this dish tastes best immediately after baking and up to a few hours later. (Chicken made this way dries out after this period.) Keep baked chicken in the turned-off oven for a couple of hours. Later transfer to the fridge for up to 24 hours, in a closed container. Reheating: reheat using your preferred method.