Mix the orange juice, olive oil, hot sauce, mustard, and orange zest together in a large bowl. Add the chicken and toss to combine. Cover with plastic wrap and let marinate for at least 1 hour and up to overnight in the refrigerator.
Prepare the grill to medium direct heat. Let chicken come to room temperature before grilling.
Drain the chicken from the marinade and pat dry. Grill on each side for 5 minutes, then turn the heat to medium-low and cover the lid of the grill. Continue cooking the chicken until it's cooked through, about 25 minutes more.
While the chicken is grilling, melt the butter in a small saucepan on the grill. Whisk in the honey, orange juice, BBQ sauce, zest, mustard and allspice. Reserve some of the glaze in a small ramekin for serving.
Brush the chicken pieces with glaze, then flip the chicken, glaze side down, and cook for 2 minutes. Brush second side of the chicken with glaze and flip again. Continue cooking for 3 more minutes. Remove the chicken from grill to a platter and serve with reserved glaze.