Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Remove the loose, papery outer skin from the head of garlic. Cut about ½-inch off the top to expose the cloves. Place the garlic head on a large square of aluminum foil and drizzle oil over the top of the cloves. Fold up the foil sides and seal to make a packet, leaving a little room for the expansion of steam. Brush the cooking grates clean. Grill the garlic over indirect medium heat, with the lid closed as much as possible, until the cloves are soft, 30 to 45 minutes. Remove from the grill and allow to cool. Squeeze the garlic from the individual cloves into a small bowl.
In the bowl with the garlic, combine the lemon zest, 1 tablespoon of the lemon juice, rosemary, salt, and pepper. Mix well.
Remove and discard the neck, giblets, and any excess fat from the chicken. Use your fingers to gently separate the skin from the meat of the chicken breast to make a space for the paste. Spread half of the paste under the chicken breast skin, spreading it gently until the meat is covered. Season the inside of the chicken cavity with salt and pepper and add the rosemary sprigs.
Truss the chicken with butcher’s twine. Pour the remaining 1 tablespoon of lemon juice and the wine into the cavity. Coat the outside surface of the chicken with the other half of the paste, pressing it into the skin.
Grill the chicken, breast side up, over indirect medium heat, with the lid closed, until the juices run clear and the internal temperature reaches 160º to 165°F in the thickest part of the thigh (not touching the bone), 1¼ to 1½ hours.
For a beautiful presentation, halfway through grilling time, carefully slide 3 lemon slices under the twine on top of the chicken breasts.
Remove the chicken from the grill and transfer to a platter. Loosely cover with foil and let rest for about 10 minutes before removing the twine and carving. Serve warm.