Preheat your Barbecue grill.
If using charcoal, the grill is ready when the coals have a gray-white ash coating. Using a poker, divided the coals into two piles, pushing each to one side of the grill. Place a pan between the coals beneath the grate to catch fat drippings and help prevent flare-ups.
If using a gas grill, leave the middle burner off and heat the side burners to medium (350 degrees F). If possible, place a pan between the flames beneath the grate to catch fat drippings and help prevent flare-ups. There was not enough room to on my gas grill to do this, but I did not have any problems with this.
While the grill heats, prepare the chicken breasts. In a medium-size bowl, combine the salt, black pepper, and brown sugar. Rub olive oil over the chicken breasts and then pat on the salt/pepper/brown sugar rub.
Arrange the chicken breasts, skin side up, over the center of the grill so the chicken pieces are not over the flames or hot coats. Cover the grill (leaving any vents open), cook for 30 minutes, and walk away. Do not open the lid of the grill for 30 minutes - Walk away!
After 30 minutes, open the grill, turn the chicken pieces over, recover the grill, and cook for another 30 minutes without opening the grill.
After the last 30 minutes, open the grill and insert your meat thermometer at the thickest part of the chicken pieces without touching the bone. Remove the chicken from the grill when the meat thermometer registers an internal temperature of 165 degrees F (juices will run clear when cut with the tip of a knife). Let the chicken breasts rest for 10 minutes before serving.
Makes 4 servings.
* This is the correct amount of salt for the recipe. As you are slow grilling the chicken, most of the salt dissolves and does not remain when the chicken is done. You could reduce the amount of salt to 3 tablespoons, if desired.
** As I do not like chicken skin, I experimented with cooking these chicken breast by leaving the skin on one and removing the skin from the other. Neither my husband or I could tell the difference in how tender and juicy they were when cooked. So, your choice on this!
Slow Grilled Chicken Breasts Recipe: https://whatscookingamerica.net/poultry/slowgrilledchickenbreasts.htm