Most polymers solidify into a glassy amorphous state, accompanied by a rapid increase in the viscosity when cooled below the glass transition temperature (T(g)). There is an ongoing debate on whether the T(g) changes with decreasing polymer film thickness and on the origin of the changes. We measured the viscosity of unentangled, short-chain polystyrene films on silicon at different temperatures and found that the transition temperature for the viscosity decreases with decreasing film thickness, consistent with the changes in the T(g) of the films observed before. By applying the hydrodynamic equations to the films, the data can be explained by the presence of a highly mobile surface liquid layer, which follows an Arrhenius dynamic and is able to dominate the flow in the thinnest films studied.