Generously salt and pepper the chicken on both sides.

Place the oil in a large enameled cat iron pot (like a le creuset durh oven) set over high heat. Add the chicken, skin side down, and cook until deeply browned, 4-5 minutes. Turn the chicken over and let it brown on the second side, another 4-5 minutes. Remove the chicken to a plate and set aside.

Turn the eat to medium and add the shallots to the pot. Cook, stirring often, until thy begin to soften, 3-4 minutes. Add a splash if the chicken stock and use a wooden spoon to loosen any bits if shallot or chicken that might be caught at the bottom if the pot. Add the remaining stock to the pot and add the chicken, skin side up, along with any juice that's accumulated in the plate. Scatter the garlic cloves, olives, thyme sprigs all over the chicken. Evenly pour the lemon juice over all. Bring the mixture to a boil, turn the heat as low as it will go, cover the pot, and cook for 1 hour, or until the chicken is nearly falling off the bo