Place chicken in a large resealable plastic bag set in a shallow dish. For marinade, in a small bowl stir together honey, mustard, lemon peel, lemon juice, oil, garlic, salt, hot pepper sauce, and black pepper. Pour over chicken in bag; seal bag. Turn to coat chicken. Marinate in the refrigerator for 4 hours, turning bag occasionally.
Drain chicken; place remaining marinade in a saucepan. Bring marinade to a boil. For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place chicken on grill rack over drip pan. Cover and grill for 50 to 60 minutes or until chicken is no longer pink (180 degrees F), brushing occasionally with sauce during the last 5 minutes of grilling. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Place chicken pieces on grill rack over burner that is off. Grill as directed.)