2 tablespoons extra-virgin olive oil
Kosher salt and lots of freshly ground black pepper
One 3- to 3 1/2-pound chicken, cut into 8 pieces or 3 pounds legs and thighs
1 large onion, chopped (about 1 cup)
8 to 10 fingerling potatoes or 2 to 3 medium Yukon gold potatoes, cut into 1 1/2-inch pieces (about 1 1/2 cups)
1/2 cup pitted chopped green olives
Brown the chicken: In a wide, heavy-based sauté or frying pan, preferably cast-iron, heat the oil over medium-high heat. Season the chicken parts well with some salt and a lot of black pepper. Add the chicken, skin-side down, and cook until the skin is well-browned and crisp, about 10 minutes. Turn the chicken, reduce the heat to medium, partially cover the pan (another pan, inverted, can take the place of a lid) and continue cooking another 15 minutes.
To finish: Add the onion to the pan with the chicken. Continue cooking, stirring the onion occasionally, for about 10 minutes. Add the potatoes, and continue cooking, stirring occasionally, until the potatoes are tender and the chicken is cooked through—the juices from a thigh pieces will run clear when pricked with the tines of a fork—another 10-15 minutes. Add the olives and cook for another few minutes just to warm them through. Serve immediately.