Season the Chicken: Rub the chicken inside and out with kosher salt and black pepper. Let it rest at room temperature while preheating the oven or leave it uncovered in the fridge for up to 24 hours for deeper flavor.
Preheat the Oven: Heat your oven to 475°F.
Prepare the Skillet: Heat a 12-inch oven-safe skillet over high heat until very hot, about 5–10 minutes. Place two lemon quarters inside the chicken cavity.
Sear and Roast: Place the chicken breast-side up in the skillet, pressing the legs flat on the skillet's surface. Drizzle with olive oil. Roast in the oven for 25–35 minutes, until the meat is not quite done (still slightly pink when a knife pierces the thigh).
Prep the Chard: While the chicken roasts, separate chard stems from the leaves. Tear leaves into bite-sized pieces and cut stems into ½-inch lengths.
Cook the Stems and Garlic: Remove the skillet and stir in chard stems and garlic. Roast for 5 minutes, stir again, and continue cooking until the stems are tender and the chicken is fully cooked, 5–15 minutes more.
Finish with Wilted Chard: Transfer the chicken to a cutting board to rest. Place the skillet over medium-high heat. Add the chard leaves, optional olives, and chile flakes, and cook until wilted, about 5 minutes.
Serve: Carve the chicken and serve with the wilted chard mixture. Drizzle with pan juices and squeeze the juice of the remaining lemon wedges over the dish if desired.