Sprinkle the chicken with 1 teaspoon salt on each side. Combine the olive oil, lemon zest, lemon juice, garlic, rosemary, and 2 teaspoons pepper in a small measuring cup. Place the chicken in a ceramic or glass dish just large enough to hold it flat. Pour the lemon marinade over the chicken, turning it in the dish. Cover the dish with plastic wrap and refrigerate for at least 4 hours or overnight. Turn the chicken 2 or 3 times while marinating.
When ready to grill, prepare a hot charcoal fire on 1 side of a grill (or turn a gas grill on low heat). Spread 1/4 of the coals across the other side of the grill. Place the chicken on the cooler side, skin side up, and weigh it down with the dish you used for marinating. Cook for 12 to 15 minutes, until the underside is golden brown. Turn the chicken skin side down, weight again with the dish, and cook for another 12 to 15 minutes, until the skin is golden brown and the chicken is cooked through. Place the lemon halves on the cool side of the grill, cut side down for the last 10 minutes of cooking. Remove the chicken to a plate or cutting board, cover with aluminum foil, and allow to rest for 5 minutes. Cut in quarters, sprinkle with salt, and serve with the grilled lemon halves.