Spices
It's all about the seasonings. Try this:
In a bowl whisk together 1/4 cup of extra virgin olive oil, 1 teaspoon each of dried thyme, rosemary, garlic powder, black pepper. Add 1/2 teaspoon of cayenne pepper if you like things spicy. Whisk it together and pour over your raw chicken breasts and let it marinate at least 2 hours before grilling.
Throw away the marinade after you use it, and DO NOT baste the chicken with it. It's important not to overcook the chicken as well.
Also, remember to trim all the fat away from the breast. Chicken fat has a musty, gamey flavor.
Oh, and those restaurants usually grill chicken over a charcoal grill, sweetened with some wood smoke. You can do the same at home, just soak some wood chips in water and wrap them in foil with some toothpick holes poked in the outside and put the whole package right on top of the heat source. I like hickory wood, but you can use any type (EXCEPT PINE!)