I agree with a lot of the folks on here as well. You want to either brine or marinate the breasts, as they do dry out easily. You don't want a really hot fire. Just close the lid and let them cook a few minutes. I've been cooking for a living for 9 years now, and cooking on a grill at home for about 13 years, and just in the past month realized that I've been cooking with WAY to much heat.
The last time I cooked chicken, I brined it, and flavored the brine with garlic, pepper, thyme, sage, and rosemary. My other half, PeppA, loved it!
Marinating in Italian salad dressing is a classic. Heck, even restaurants do that.
Try some different marinades. Buy some, or make some. Jamaican Jerk is good, although spicy. Have you tried Teriyaki or some other Asian inspired flavor?
You can also brine, then before you cook, remove it from the brine, pat it dry with paper towels, and apply a dry rub or other seasoning mixture.
This possibilities are practically endless. Chicken is a good "blank canvas" for different flavors. Just don't over cook them. If you have a probe thermometer, your target temperature is 160 degrees F. Carry-over cooking will take it up to 165 degrees F, the recommended minimum safe temperature for chicken.