Arranging the grill to provide two levels of heat, in this case medium-high and low, allows you to brown the meat and also cook it through without torching the poor bird beyond recognition. This is easy on a gas grill: You start the chicken over medium-high heat and move it to low (or adjust the burners to low) after it has browned.
It's also easy to do this on a charcoal grill, though it takes a modicum of planning: Start by lighting the charcoal - I prefer a chimney starter - and burn until the coals are covered with a thin coat of gray ash. Spread out the charcoal in the grill, but leave at least a third of the grill empty or with just a few coals. Using long-handled tongs, arrange the coals so they are about two deep on the hot side. Even on the cooler side, there will be enough heat to continue cooking the chicken, but not so much that the exterior burns.
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