Self-diffusion in thin solution-cast films of nearly symmetric block copolymer was probed by forward recoil spectrometry, both above and below the bulk order-disorder temperature. Diffusion in the as-prepared films is characteristic of diffusion in an isotropic medium. The diffusion coefficient is lower than the diffusion coefficient for a homogeneous melt but shows no discontinuity at the ordering temperature. The mobility of a certain fraction of the copolymer chains is reduced dramatically by annealing the as-prepared films before allowing the diffusion to take place. This slowing down of the diffusion process is assumed to be associated with the preferential orientation of lamellar domains parallel to the film surface. Diffusion in the direction perpendicular to the lamellae is much slower than diffusion parallel to the lamellae, and the diffusion process in the preannealed samples can only be modeled by using two very different values for the diffusion coefficient.