Heat oil in a medium, heavy saucepan over medium heat.

Add the onion and garlic and cook, for about 10 minutes or until soft

Add the vinegar, Worcestershire, brown sugar, mustard, cayenne, salt and pepper and bring to a simmer

Lower heat and cook for 5 minutes

Add the ketchup and cook for another 5 minutes, stirring constantly at the end to avoid sticking

Set aside

CHICKEN
Light the grill, and while you wait for the coals to burn down, squeeze lemon all over the chicken pieces, and then season them lightly with he dried thyme and salt and pepper.

Arrange the chicken, skin side down, over a medium hot fire.

Cook covered for 10 minutes

Turn the chicken and then cook the other side, covered, for 15 minutes

Open the grill, and generously brush barbecue all over the skin side of the chicken pieces

Turn and grill, basting with sauce, and turning occasionally, until glazed with sauce and browned, about 10 minutes

Serve immediately