The presence of interfaces and geometrical confinement can have a strong influence on the structure and morphology of thin films of semicrystalline polymers. Using surface-sensitive grazing incidence wide angle X-ray scattering and atomic force microscopy to investigate the vertical structure of thin films of poly(3-hexylthiophene) crystallized from the melt, we show that highly oriented crystallites are induced at the air/polymer interface and not as sometimes assumed at the interface to the substrate. These crystallites are oriented with their crystallographic a-axis perpendicular to the plane of the film. While the corresponding orientation dominates in thinner films, for sufficiently thick films (>60 nm) a layer containing unoriented crystals is present below the surface layer. Due to the anisotropic charge transport properties, the observed effects are expected to be of special relevance for potential applications of semiconductor polymers in the field of organic photovoltaics for which vertical transport in thicker films plays an important role.