Self-organized superlattices are observed in GaInAsSb epilayers grown nominally lattice matched to vicinal GaSb substrates. The natural superlattice (NSL) is detected at the onset of growth; is continuous over the lateral extent of over several microns; and persists vertically throughout several microns of the epilayer. Furthermore, the NSL is inclined by an additional 4(sup o) with respect to the vicinal (001) GaSb substrate. The tilted NSL intersects the surface of the epilayer, and the NSL period is geometrically correlated with surface undulations. While the principle driving force for this type of phase separation arises from solution thermodyamics, the mechanism for the self-organized microstructure is related to local strains associated with surface undulations. By using a substrate with surface undulations, the tilted NSL can be induced in layers with alloy compositions that normally do not exhibit this self-organized microstructure under typical growth conditions. These results underscore the complex interactions between compositional modulations and morphological perturbations.