About 1 hour before cooking, soak hickory chips in enough water to cover.
In a covered grill mound the briquettes, ignite. When ready, arrange the coals in a circle leaving the center open; insert a foil drip pan. Test for medium coals (4-second count) over the drip pan.
Meanwhile, for sauce, in a small saucepan cook onion in hot butter or margarine until tender but not brown. Stir in cornstarch. Add tomato sauce, vinegar, honey, dry mustard, salt, and pepper. Cook and stir until thickened and bubbly, then cook and stir 2 minutes more.
Halve chicken. Season with salt and pepper. Drain hickory chips, then sprinkle half over the coals. Place chicken on the grill, skin side up, over the drip pan. Brush with sauce. Cover and grill 30 minutes. Brush with sauce and add remaining chips; grill 25 to 35 minutes more or until done (180 degrees F). Transfer to a serving platter, brush with sauce. Pass remaining sauce. Makes 6 servings.