Set the EGG for indirect cooking (with the convEGGtor) at 400°F/204°C.
Rinse the chicken under cold water and blot dry with paper towels. Place the chicken in a Roasting & Drip Pan. Generously season the neck and cavities with salt and pepper. Place 2 garlic cloves in the main cavity along with 1 of the lemon halves and a sprig of rosemary. Place a third garlic clove in the neck cavity.
Concentrating on the breast, rub the chicken with the cut side of the garlic, remaining lemon half and the butter or olive oil. Generously season the bird on all sides with salt and pepper. Truss the chicken, then place breast side up in the pan. Add the garlic halves, lemon half and rosemary, with the cut side of the garlic and lemon facing the bird.
Place the chicken in the EGG and roast it until the skin is crisp and golden brown and the meat is cooked through, 1 to 1 1⁄4 hours. After 30 minutes, start basting the bird with the juices that accumulate in the bottom of the pan.
Roast until the internal temperature reaches 165°F/74°C. Lay a piece of foil over the breast if it starts to brown too much before the bird is fully cooked.
Transfer the chicken to a cutting board and let it rest for about 5 minutes. Remove the trussing string before carving the bird.