Place all of the ingredients for the sauce in a small pot and bring to a bubble. Reduce heat to low and let thicken for 30 minutes. When the sauce is done, prepare the chicken.
Remove the skin from the chicken pieces and discard. Arrange chicken on broiler pan or on a cooling rack set over a baking sheet. Place rack in center of oven and preheat broiler.
Dress chicken pieces lightly with EVOO and season with salt and pepper. Broil 20-25 minutes, turning occasionally until juices run clear. Baste chicken very liberally with sauce and broil for another minute or 2 to set the sauce.
Garnish BBQ chicken with chopped scallions and serve.