Cut each chicken piece lengthwise into 3 strips. Place chicken in a resealable plastic bag set in a shallow dish.
For marinade, in a small bowl stir together oil, hot pepper sauce, parsley (if desired), honey, salt, cayenne pepper, black pepper, and garlic.
Pour 2 tablespoons of the marinade over chicken; seal bag. Marinate in the refrigerator for 30 minutes to 24 hours, turning bag occasionally. Cover and chill the remaining marinade for basting.
Drain chicken, discarding marinade. Just before grilling, cut each potato lengthwise into 8 wedges. Lightly brush wedges with some of the reserved marinade.
Place potatoes on the rack of an uncovered grill directly over medium coals. Grill for 15 minutes.
Place chicken on grill rack next to potatoes. Grill for 9 to 12 minutes more or until chicken is no longer pink (170 degrees F) and potatoes are tender, turning and brushing chicken once with the reserved marinade halfway through grilling.