In a bowl whisk together the vinegar and the salt, add the oil in a stream, whisking, and whisk in ½ cup of 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.

Grill the chicken on an oiled rack set for 10-15 minutes on each side, or until it is cooked through (internal temp is at least 165° F), baste it with some of the barbecue sauce, and grill it, turning it, for 2 minutes more.

Serve the chicken with the remaining sauce.

Make maple barbecue sauce:

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.

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.