The question of how bulk electronic order is terminated at a surface is an intriguing one, and one with possible practical implications--for example in nanoscaled systems that may be characterized by their surface behaviour. One example of such order is orbital order, and in principle it should be possible to probe the termination of this order with surface X-ray scattering. Here, we report the first observation of the scattering arising from the termination of bulk orbital order at the surface of a crystal--so-called 'orbital truncation rods'. The measurements, carried out on a cleaved perovskite, La(0.5)Sr(1.5)MnO(4), reveal that whereas the crystallographic surface is atomically smooth, the orbital 'surface', which is observed through the atomic displacements caused by the orbital order, is much rougher, with a typical scale of the surface roughness of approximately 7 degrees A. Interestingly, the temperature dependence of this scattering shows evidence of a surface-induced second-order transition.