Heat grill to medium-high; lightly oil grates. Place chicken in a medium bowl; season with salt and pepper. Pour 1/4 cup barbecue sauce over chicken, and toss to coat. Divide remaining barbecue sauce between two bowls (1/4 cup each); use one for basting and the other for serving.
Grill chicken, turning and basting occasionally with reserved basting sauce, 8 to 10 minutes total. Remove chicken from grill; serve with reserved serving sauce.