Heat your barbeque to medium-high. With kitchen shears or a knife, cut along either side of the chicken's backbone and remove it. Place the chicken skin-side down, on a cutting board, and firmly press it flat. Brush the chicken with olive oil and season with salt and pepper. Place the chicken, bone-side down, on the barbecue. Cook 3 to 4 minutes and then turn the chicken over. Cook the skin-side until the chicken achieves a nice sear, but is not overly dark.
Turn the chicken skin-side up again and move it to one side of the barbeque. Turn the heat off underneath it; leave the other side set to medium-high. Cover and barbecue the chicken until cooked through, about 35 minutes (when cooked, the temperature of the chicken should register 170 degrees F on an instant read meat thermometer inserted deep into the thigh). Uncover and baste the chicken with barbecue sauce. Heat through for a few minutes and then transfer the chicken to a platter. Allow it to rest a few minutes before cutting into portions.