To make the glaze, heat oil in a large frying pan over medium heat and sauté onions and garlic for 10 minutes, or until onion is soft. Add remaining glaze ingredients and bring to a boil. Reduce to a simmer, then cover and cook for 15 minutes, or until richly flavored and reduced to 4 cups (1 liter). Transfer to a food processor or blender and process until smooth. Measure out 2 cups (500 ml) to use as a glaze; set aside remainder to serve with the chicken.
Preheat a barbecue to medium. Sprinkle the salt over chicken. Barbecue chicken 15 cm (6 inches) from the heat for 15 minutes, turning often, until browned all over.
Brush chicken pieces with 1 cup (250 ml) glaze, turn over, then brush with remaining glaze. Barbecue, without turning, for 5 to 7 minutes, until chicken is cooked through.
Serve chicken with the reserved barbecue sauce.
Discard any unused glaze that remains after the chicken is cooked. Don't add it to the sauce you're serving at the table, because the glaze has been in contact with raw chicken via the basting brush and will contain bacteria.
Cut-up whole chickens are a good choice for a crowd because there's something to please everyone. As you're barbecuing, be sure to check the white-meat (breast) portions first for doneness, as they cook more quickly than dark (leg) meat.