Use any olives with pits that you like; the Italian Castelvetrano bright green olives are sweeter than most olives, with a meaty bite. Chicken breast, legs, and/or wings will also work here, but white meat won’t be as succulent. This recipe is based on David Tanis’ in The New York Times.
Heat the oven to 375°F. In a large ovenproof skillet (ideally with a lid), heat the butter and oil over medium high heat. Pat the chicken thighs dry with paper towel and season all over with salt and pepper.
Place the thighs skin side down in the hot pan and cook, without disturbing, until the thighs lift easily from the pan and the skin is deep golden brown, about 5 minutes. Turn the chicken over and sear for another few minutes, until golden. Take care not to burn the skin or the oil by adjusting the heat down a bit.
Remove the thighs to a plate and pour off all but a tablespoon of the fat. Return the pan to medium heat and deglaze the pan by pouring the chicken stock in and scraping up any browned bits as the stock comes to a boil.
Return the thighs to the pan skin side up. Season with the red pepper flakes and fennel seeds, then smear with the garlic. Arrange the lemon wedges and olives around the chicken, squeeze a couple of the wedges over the chicken and into the drippings.
Cover the skillet with foil or lid and place on the center rack in the hot oven. Bake for about one hour, or until chicken is very tender and juices run clear.
Arrange the chicken, olives, and lemon wedges on a platter and tent with foil. Return the skillet to medium heat and spoon off as much fat as possible. Bring the pan juices to a boil and reduce for about a minute. Pour over the chicken, dust with chopped parsley, and serve immediately.