Rinse the chicken and pat dry. Blend 2 tablespoons oil with salt, pepper, cumin, oregano, paprika and cayenne. Rub each piece with the paste and refrigerate at least 20 minutes.
In a heavy ovenproof casserole with a lid, heat the remaining 2 tablespoons oil. Fry the chorizo over medium heat until crispy and its fat renders. Drain on paper towels.
Brown the chicken skin side down, then on all sides, about 10 minutes. Set aside.
Make a sofrito by sauteing the onion, garlic, bell pepper and bay leaves until very soft and almost dissolved. Stir in the rice to coat the grains.
Add the tomatoes and broth and season with salt and pepper. Return the chorizo and chicken, bring to a boil and simmer 5 minutes.
Cover and bake 20 minutes, until the chicken is done and the rice is tender and has absorbed the liquid. Scatter the olives on top before serving.