1. Blend lemon juice, oil, garlic, and rosemary leaves in a blender until rosemary is finely chopped.

2. Divide chicken pieces between two large resealable plastic bags, and set in two large bowls (to catch any drippings). Divide rosemary marinade between bags. Marinate chicken in refrigerator, turning bags occasionally, 8 to 12 hours.

3. Remove chicken pieces from bags, reserving marinade in a bowl.

4. TO GRILL: Place rosemary sprigs on coals (if using a charcoal grill) or on lower rack (if using a gas grill); heat grill until medium-hot. Grill chicken pieces (on upper rack, if using a gas grill), skin sides up, basting with reserved marinade and sprinkling with 2 1/4 teaspoons salt, 15 minutes (move pieces around grill so as not to char). Turn pieces over; continue to grill, sprinkling with 2 1/4 teaspoons salt and squeezing juice from 2 lemon halves over chicken, until golden brown and cooked through, 15 to 30 minutes more.

TO ROAST: Preheat oven to 425 degrees, with racks in upper and lower thirds. Divide the rosemary sprigs between two large rimmed baking sheets, spreading into a single layer on each. Place 6 chicken pieces on each sheet; sprinkle with 2 1/4 teaspoons salt. Roast in upper and lower thirds of oven, basting twice with reserved marinade, 20 minutes. Switch position of sheets. Squeeze juice from 2 lemon halves over chicken; sprinkle with 2 1/4 teaspoons salt. Continue to roast until golden and cooked through, 20 to 25 minutes more.

5. Discard any unused marinade. Loosely tent chicken with foil, and let stand 10 minutes. Cut chicken legs from thighs, and halve breasts crosswise.

6. Arrange chicken on a large platter; garnish with rosemary sprigs and remaining 6 lemon halves.