Chicken breasts are great on the grill, healthy, and affordable. Bone in chicken breasts are often on sale for $1 a pound. Even if you don't eat the skin for health reasons, it helps keep the breast moist during cooking. Dryness is a big complaint people have with chicken breasts. This is a piece of meat that will benefit greatly from the use of an instant read thermometer. Do not cook your chicken breast past 160-165. Dark meat can handle being cooked further because of the fat content, but not the white meat.
You can also help keep your chicken breasts (and other lean meat) moist by using a brine. The basic formula I use for a small batch is to heat 1/4 cup kosher salt, 1/4 cup sugar, and 4 cups of water until everything is dissolved, cool, then add my meat for at least 6 hours, rinsing well before using. I usually add spice to the brine too like pepper corns, bay leaves, thyme, etc. Here are the breasts after soaking overnight in the brine solution.
Chicken breasts should be cooked hot and fast with indirect heat. Here they're placed on the cool side of the grill. The opposite side has a chimney full of hot lump and a foil pouch with a blend of apple and cherry woods. With the intake set to about 1/3rd open the grill will run at about 400 degrees. The chicken will be done in about an hour.
Once you breasts reach 160 you might want to put them skin side down over the coals for about 30 seconds to finish crisping up the skin. Watch it closely, it will go from crispy to black in seconds.