Preheat the oven to 450°F. Place a 13 × 9-inch roasting pan in the oven.

Rinse the chicken and use paper towels to pat it dry, inside and out.

Squeeze 1 of the lemon quarters over the skin and rub the juice around with your fingers. Using your fingers to gently separate the skin from the breast, place a couple of the garlic cloves and some of the lemon zest under the skin of the breast on each side.

Let it sit about 10 minutes, then pat the bird dry again, rub the skin with 2 tablespoons olive oil, and season with the salt, pepper, red pepper, and some of the chopped rosemary.

Make an incision on the inside of each thigh and insert a garlic clove. Place 3 of the garlic cloves in the cavity, along with the rosemary sprigs and 2 of the lemon quarters.

You may tie the legs together over the cavity, if you like. Place the chicken breast side up in the preheated roasting pan.

Bake for about 30 minutes, watching to make sure the chicken starts to brown.

Carefully loosen the chicken from the pan with a spatula and turn it over to brown the underside.

At this point, lower the oven heat to 400°F. Add the remaining tablespoon olive oil to the pan, then scatter the onion, olives, remaining garlic, lemon quarters and zest, and chopped rosemary around the chicken and cook for about 15 minutes.

Turn the chicken over again and stir the onion, olives, and garlic around a little. Cook another 10-15 minutes to re-crisp the skin.

When the chicken is a deep golden brown, remove it from the oven and let it sit for about 5 minutes.

Transfer the chicken to a plate and collect any juices that drain. Tilt the roasting pan and spoon off the fat, if desired. Stir the olives, onion, and lemon around, pressing on the lemon a little to extract the juice. Add the chicken juices to the pan and scrape the brown bits off the bottom of the pan to incorporate them into the mixture. Spoon the juicy olive-onion mixture around the chicken and serve.