Rub chicken all over with barbecue rub. Fire up smoker or grill to 225 degrees F, adding chunks of smoking wood when at temperature. When wood is ignited and producing smoke, place chicken in smoker or grill, skin side up. Smoke until an instant read thermometer reads 160 degrees F when inserted into thickest part of thigh, 1 1/2 - 2 hours. Remove from smoker and let cool completely, about 1 hour.
