In a small saucepan, cook and stir onion and butter over medium heat until onion is tender. Stir in ketchup, water, honey, lemon juice, Worcestershire sauce, and black pepper. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes. Transfer sauce to a covered storage container. Cover and chill up to 24 hours. Pack in coolers with ice to tote.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken, bone sides down, on grill rack over the drip pan. Cover and grill for 40 to 50 minutes or until chicken is no longer pink (170 degree F), brushing occasionally with sauce during the last 10 minutes of grilling. (For a gas grill, preheat grill. Reduce heat to medium. Adjust heat for indirect cooking. Grill as above.) Serve with remaining sauce. Makes 4 to 6 servings.