There is a reason why people tend to avoid grilling chicken breasts on the BBQ. More often than not without some special care chicken breasts turn out dry, tasteless, and just unappealing. The lack of skin and bone leaves no barrier for keeping moisture in, and thus dry tasteless chicken breasts are far easier to produce than moist flavorful ones are.
Fortunately this does not have to be the fate of those beautiful chicken breasts you came home in hopes of tossing on the BBQ. There are a few tips and tricks that will ensure that your chicken comes off the grill tasting amazing, and leaving you never afraid to grill chicken breasts again.
1) Good chicken starts with good seasoning. Flavor must be infused into your chicken to ensure it takes on a brand new flavor profile. Rubs are a great choice as is a good marinade. Marinades and brines can be done overnight, to encourage the meat to take up extra moisture. Infuse the moisture with the seasonings you want. Rubs should be put on about a couple of hours before grilling. These will add a more intense blast of flavor in a shorter period of time.
2) Part of the problem with cooking chicken breasts on the grill, is they are thick, and must be cooked a long time to get them cooked all the way through. By the time the chicken is cooked it is also very dry and flavorless. There are two remedies to this problem, you can either butterfly or tenderize the chicken, making it thinner and thus ensuring it cooks faster, or you can cook the skinless, boneless breasts over indirect heat, at a slower rate. They will take a bit longer to cook this way, but it will prevent the charring of your meat that leaves it tasting so dry.

3) When grilling chicken whether over charcoal or propane, heat only one side of the grill. In the case of charcoal, your coals should be heaped up on one side of the grill. This gives the grill a hot side and a cooler side. Put your chicken on the indirect heat and allow them to cook slowly.
4) Let the breasts cook on one side without flipping until the meat reaches 150 degrees. Then turn the chicken, placing it on the direct heat side of the grill, and baste it with your favorite barbeque sauce. Continue to turn and baste chicken, never allowing it to dry out until the internal temperature of the chicken reaches 165.