Place in a pot, balsamic vinegar, ketchup, brown sugar, garlic, Worcestershire sauce, Dijon mustard, salt and pepper.
Cook over medium heat until reduced to 1/3, for about 15 minutes. Reserve ½ cup of the sauce for serving time.
Season chicken, cut in pieces: breasts, wings, legs and thighs, with salt and pepper.
Roast chicken pieces on the grill for 10 minutes each side, brushing them with BBQ sauce 2 to 3 minutes per side.
Place chicken in a serving dish with the reserved sauce.