GaSe, a layered semiconductor, may be grown on the Si(111) surface by molecular beam epitaxy. The crystalline quality is relatively good, in the sense that the MeV4He ion minimum channeling yield (~30%) is as low as that of state-of-the-art bulk material, and the interface is atomically abrupt. The initial film deposits are epitaxial islands, and subsequent growth is in the Frank-van der Merwe mode. With the islands already relaxed at the nucleation stage and coalescing to essentially uniform coverage with the first monolayer of deposition, GaSe on Si(111) provides an example of van der Waals epitaxy. However, it is difficult to understand how epitaxy (crystallographic alignment with the substrate) can occur in such a case, where the film is incommensurate starting from the initial nuclei. A mechanism for alignment of the islands is proposed: they are aligned with the silicon substrate through the influence of dangling bonds at their perimeter, being "quasi-commensurate" by virtue of their small lateral size. Although discommensurate regions are created as the islands grow laterally, there is simply no change in their orientation.