Using Monte Carlo and molecular dynamics simulations, we have investigated the dynamics of a model glass-forming polymer undergoing physical aging confined to a free-standing thin film. When a glass-forming material is cooled below its glass transition temperature Tg it falls out of equilibrium, and its physical properties (internal energy, dynamic properties) will gradually evolve towards their equilibrium values in a process known as physical aging. We have found that in free-standing thin films of polymer glasses, which have a Tg reduced from the bulk polymer, the free surface can rapidly reach equilibrium while material that is only approximately 10 nm from the surface exhibits a bulk-like equilibration process.