It is shown that the presence of highly charged impurity ions strongly increases the collisional damping of zonal flows in a low-collisionality tokamak plasma. A formula for the zonal flow damping time is derived, which indicates that the damping is enhanced approximately by a factor Zeff. If the aspect ratio is large, the enhancement is significantly larger. The zonal flow damping time is also the time which the poloidal plasma rotation needs to respond to a sudden change in the pressure gradients.