Step 1

In a bowl whisk together the vinegar and the salt, add the oil in a stream, whisking, and whisk the marinade until it is emulsified. Divide the chicken pieces between 2 large bowls, pour the marinade over them, and let the chicken marinate, covered and chilled, overnight.

Step 2

Grill the chicken on an oiled rack set about 4 inches over glowing coals for 10 minutes on each side, or until it is cooked through, baste it with some of the barbecue sauce, and grill it, turning it, for 2 minutes more. Serve the chicken with the remaining sauce.

Step 3

In a large heavy saucepan combine the onions, the oil, the Worcestershire sauce, the mustard, the ketchup, the broth, the vinegar, and the syrup, bring the mixture to a boil, and simmer it, stirring occasionally, for 50 minutes, or until it is reduced to about 3 1/3 cups. The sauce may be made 1 week in advance and kept covered and chilled. Makes about 3 1/3 cups.