Grilling bone-in chicken breasts is trickier than it seems. You want well-browned, crisp skin as well as moist meat. The challenge is the thick part of the breast, which is quite slow to cook, while the tapered end cooks quickly. Adding a glaze to that equation makes the situation even a little thornier.
First, the chicken breasts are brined to boost their moistness and to season them. Second, the grill is set up with a modified two-level fire; the hot side is used for browning and crisping, and the cooler side for the bulk of the cooking time. Finally, the glaze is applied to the chicken breasts only in the final minutes of grilling, so that the sugars won't burn.
Once you master this basic technique for grilling chicken breasts, you can apply any number of glazes or sauces, even barbecue sauce, if you like.