In-situ grazing incidence X-ray diffraction has been used to investigate the kinetics of crystallization at the surface of thin films of poly(ethylene terephthalate) (PET). By varying the angle of incidence of the X-ray beam around the critical angle of the film, the penetration depth can be tuned to allow a direct comparison of molecular ordering in the surface and bulk of the film. The results show that ordering occurs significantly faster at the surface in the temperature range 90-100 degrees C (close to the bulk glass transition temperature of 75 degrees C). The (0 (1) over bar1) and (010) peaks narrow more rapidly and achieve a lower width, indicating that the crystallization progresses more rapidly in these crystallographic directions. This enhanced ordering is attributed to a combination of surface energy effects, which promote localized packing, and to an enhanced segmental mobility near the free surface.