Preheat the oven to 375 F. Season the chicken  with half the salt and the pepper. 

In a large cast-iron skillet enameled pan, heat the oil over medium-high heat. When shimmering, add half of the chicken skin side down. Top the chicken pieces (not the pan) with a heavy pot lid or another pan. Cook over moderate heat until golden brown and crisp, 5 to 7 minutes. 

Transfer chicken skin side up to a large baking dish (preferably with a lid). Repeat with the remaining chicken. Scatter the olives, garlic, red onion, lemon slices and thyme in the baking dish.

In a small bowl, whisk together the oil from the pan, apple cider vinegar, bone broth, and remaining salt. Pour the mixture around the chicken. Cover tightly with foil and braise in the oven for 1 hour, until the chicken is very tender. 

Uncover and increase the oven temperature to 400°. Roast the chicken for 15 minutes longer, until the skin is crisp.

Transfer to plates and serve.