The influence of the free surface on the structure of the hexagonal lyotropic mesophase (H-1) of the binary surfactant system pentaoxyethylene-n-dodecylether + water was probed by grazing incidence X-ray diffraction. The reflected diffraction patterns consist of hexagonally arranged discrete spots showing that the orientation of the (01) lattice planes is parallel to the surface. This orientation extends several micrometers into the bulk. We report on experimental evidence for the coexistence of two lattices with different d-spacings. In the reflected diffraction patterns observed at a limited penetration depth of the incident beam, the Bragg spots split into two well-resolved peaks, one of which disappears as the penetration depth is increased. Analysis of the diffraction data reveals the existence of a surface layer of hexagonally packed micelles with a lattice constant smaller than the corresponding bulk value.