We use small-angle X-ray scattering to investigate the structures under shear of surfactant hexagonal phases swollen with oil. Rheology studies of these materials indicate a shear-induced transition between two states of different viscosity. In the low shear regime, the cylinders are preferentially oriented along the flow and the hexagonal phase exhibits a polycrystalline texture. Unexpectedly, a high shear has the effect of melting the long-range two-dimensional (2D) order of the cylinders, leading to a 2D liquid of cylinders strongly aligned along the flow.