Normally if you don't puncture the meat while you are grilling (or even baking) it will hold the moisture in. Once you do though it will dry out.
Sometimes we even boil the chicken before hand in a little bit of crab boil for about 5 mins at a rolling boil

It gets spicy if you do that though.
The biggest thing for me is the flare ups that excess fat will cause even when you don't have it directly on the flame. It usually results in a few creole pieces (aka burned

)