Heat barbecue to medium. In a large bowl, mix the carrot, cabbage, onion, ranch dressing, parsley, lemon juice and 1/4 tsp (1 mL) each salt and pepper. Separate bun halves and set aside.
Place the chicken pieces in a shallow bowl with the olive oil and remaining salt and pepper and turn to coat. Grill the chicken until cooked through, approx. 3 to 4 min. per side. On final turn, brush chicken with barbecue sauce until coated on both sides.
Meanwhile, lightly grill the buns. Divide the chicken among the 4 buns and top with the coleslaw.
No bbq? On a foil-lined baking sheet, broil chicken for 4 to 5 min. per side. Turn once and brush with sauce halfway through.