How to Make It
Preheat the oven to 400°, with the rack positioned in the center. Loosely tie the legs together with kitchen twine and tuck the wing tips under. Put the chicken in a large bowl and rub it inside and out with the garlic halves. Place the garlic and 3 oregano sprigs in the cavity.
Stir together the olive oil, shallot, 1 tablespoon chopped oregano, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Loosen the skin near the cavity with your hands; spread some of the oil under the skin. Pour the remaining oil mixture over the skin to coat. Transfer the chicken to a Dutch oven. Squeeze juice from 1 lemon half over the chicken; and place in the cavity. Season the bird evenly with 1 teaspoon of salt and another 1/4 teaspoon pepper.
Quarter the onions and potatoes; arrange around the bird. Add the black olives to the surrounding vegetables. Tuck two lemon slices between each of the wings and breasts and scatter the remaining slices from 1 lemon over the vegetables. Sprinkle the vegetables with 1/2 tablespoon of oregano and pour the wine and stock into bottom of the Dutch oven.
Roast the chicken and vegetables for 30 minutes, then lower the temperature to 325° and continue cooking for 45 minutes, basting 2 or 3 times with the pan juices until an instant-read thermometer into the thickest part of the chicken thigh registers 165°.
Remove the chicken from the oven, and let stand for 10 minutes. Carve and arrange pieces on a serving platter with the roasted potatoes, lemon slices, onions, and black olives.