If applicable, remove neck and giblets from chicken, and reserve for another use. Pat chicken dry with paper towels. Brush cavity and outside of chicken with oil. Stir together BBQ Rub and salt; sprinkle mixture inside cavity and on outside of chicken. Chill chicken 30 minutes to 12 hours.
Let chicken stand at room temperature 30 minutes. Light 1 side of grill, heating to 350° to 400° (medium-high) heat; leave other side unlit. Open beer. Place chicken upright onto beer can, fitting can into cavity. Pull legs forward to form a tripod, so chicken stands upright.
Place chicken upright on unlit side of grill. Grill, covered with grill lid, 1 to 1 1/2 hours or until golden and a meat thermometer inserted in thickest portion registers 165°. Carefully remove chicken from can. Cover chicken loosely with aluminum foil; let stand 10 minutes before serving.