Fill a chimney starter to the rim with charcoal and burn the charcoal until it is lightly covered with ash. Spread the charcoal in a tightly packed, single layer across one-half of the charcoal grate. Put the cooking grate in place, close the lid, and let the charcoal burn down to high heat (450° to 550°F). Leave all the vents open. If you are using a gas grill, preheat your grill on high until it reaches 500°F.
In a medium bowl combine the chicken pieces with the oil, salt, and pepper and mix well. Thread the chicken pieces through their centers on the top half of the skewers. The chicken pieces should touch, but do not cram them together. Refrigerate until ready to grill, or as long as 2 hours.
In a small saucepan mix the sauce ingredients. Bring to a boil over medium-high heat and cook until the liquid is reduced to ½ to ¾ cup, about 5 minutes, stirring once or twice. Remove the saucepan from the heat.
Brush the cooking grates clean. Place a strip of aluminum foil on the cooking grate over the empty section of the charcoal grate or over an unlit burner. Grill the skewers over direct high heat, with the bare wooden section of the skewers placed over the foil. Close the lid and cook until the meat is lightly charred on the surface, 4 to 5 minutes, turning once and swapping their positions as needed for even cooking. Open the lid and begin turning and basting the chicken with the sauce (you may not need all of the sauce) until fully cooked, 3 to 5 minutes longer. Remove from the grill and serve warm.