Preheat your grill for medium-high heat. Set up the grill for indirect grilling (i.e., no coals or burners directly under the chicken), and lightly oil the grate.
Open the can of sodium-free chicken broth and pour out (or drink) about half of the broth.
Rinse the chicken under cold running water and blot dry with paper towels. Rub the chicken lightly with olive oil then rub inside and out with the dry spices.
Lower the chicken onto the opened chicken broth can so the can fits into the cavity. Position the chicken so it's sitting up; you can use the legs to help it stay upright.
Place chicken on the preheated grill. Use a drip pan under the bird to prevent any flare-ups. Cook the chicken over indirect medium-high heat for about 1.5 to 2 hours, or until the internal temperature registers 165°F in the breast area and 180°F in the thigh, or until the thigh juice runs clear when stabbed with a sharp knife.
Remove from grill and let rest for 10 minutes before carving.
Serve with lemon wedges and fresh rosemary sprigs, if desired.