The surface relaxation dynamics of supported star-shaped polymer thin films are shown to be slower than the bulk, persisting up to temperatures at least 50 K above the bulk glass transition temperature T_{g}^{bulk}. This behavior, exhibited by star-shaped polystyrenes with functionality f=8 arms and molecular weights per arm M_{arm}<M_{e} (M_{e} is the entanglement molecular weight), is shown by molecular dynamics simulations to be associated with a preferential localization of these macromolecules at the free surface. This new phenomenon is in notable contrast to that of linear-chain polymer thin film systems, where the surface relaxations are enhanced in relation to the bulk; this enhancement persists only for a limited temperature range above the bulk T_{g}^{bulk}. Evidence of the slow surface dynamics, compared to the bulk, for temperatures well above T_{g} and at length and time scales not associated with the glass transition has not previously been reported for polymers.