Place chicken thighs, skin side down, on oiled grates over lit side of the grill. Grill, covered, until skin is well marked and crispy, 5 to 6 minutes. Turn thighs over, and transfer to unlit side of grill. Grill, covered, until a thermometer registers 165°F when inserted into thickest part of a chicken thigh, 20 to 25 minutes, turning halfway through grilling. Halfway through the cook time, use a brush to baste the tops of the chicken thighs with the BBQ sauce, reserving 1 cup for serving. Then, during the final two minutes of cook time, baste the tops one last time. Remove from grill, and let rest 5 to 10 minutes before serving.