The energy of segregation of Cr from the bulk to the topmost surface layer in dilute Fe-Cr alloys is endothermic but small. On the other hand, the segregation energy from the bulk to the subsurface layer is not only endothermic but relatively large. Thus, the subsurface layer presents a huge barrier, not only for the segregation of Cr from the bulk to the surface, but also for its diffusion from the surface into the bulk. This means that the topmost layer alone cannot be used to determine the barrier for Cr segregation (the segregation energy), which is determined in these alloys by the subsurface layer. We present the results of our ab initio electronic structure calculations on the segregation of Cr as an impurity in Fe, which shed some light on the origin of this anomalous behavior. We find that the interaction of a Cr atom situated in the subsurface layer, in contrast to those in the other layers, is quite complex with its nearest neighbor Fe atoms due to the magnetism of both Fe and Cr, leading to a highly unfavorable electronic structure. This in turn leads to a large endothermic energy of solution of Cr in the subsurface layer. These results are important for a proper understanding of the properties of the technologically important class of Fe-Cr steels with low concentrations of chromium.