Whisk together the water and salt in an 8-quart or larger container. Add the chicken, cover, and refrigerate for at least 12 hours and up to 24 hours.
Soak the wood chips, if using, in water for 30 minutes.
If using a charcoal grill, about 1 hour before grilling the chicken, set up your grill for indirect grilling (which basically means putting the pile of coals on one side and nothing on the other side).
Combine the lemon slices, rosemary, garlic, oil, and pepper in a food processor or mortar or molcajete or a heavy bowl and use a pestle or back of a wooden spoon to slowly but firmly mash the ingredients together until pulpy and mushy.
Remove the chicken from the brine, rinse under cold water, and pat dry with paper towels. Rub the lemon mixture onto the skin and let stand at room temperature for 15 minutes.
Place the chicken on the grill directly over the heat. Grill 7 minutes or until grill marks and some charring appear. Turn the chicken over and grill for 7 more minutes.
Using tongs, move the chicken to the cool side of the grill. If using wood chips, sprinkle them over the hot coals or fashion them into a packet made of aluminum foil and pierce the packet several times. Grill, covered with grill lid, for 1 to 1 1/2 hours or until a meat thermometer inserted into thickest portion registers 165°F (74°C).
