MoO3 is a versatile catalyst for oxidation reactions that consists of bilayers connected by van der Waals interaction. In principle a MoO3 nanocrystal can be exfoliated to create twodimensional ribbons. For this article, we study the difference between the chemistry of slabs having a variety of crystal faces and that of the edges of ribbons cut from a two-dimensional bilayer. As a descriptor of chemical reactivity we use the energy of oxygen-vacancy formation: the easier it is to form an oxygen vacancy, the better oxidant the face of a slab or the edge of a two-dimensional ribbon is. We find that the properties of ribbon edges are different from those of the corresponding slab surfaces. The surface energies of slabs are in the order (010)s < (100)s < (101)s < (001)s, whereas the edge energies of ribbons are in the order <100>r ~ <101>r < <001>r (the subscript s indicates a slab and r, a ribbon). Among the surfaces studied, we have found that (001)s and (101)s faces have the lowest oxygen-vacancy formation energies, and (010)s has the highest. In contrast, among the edges studied, <101>r has the lowest vacancy formation energies. Our calculations suggest that no benefit is obtained by creating <100>r or <001>r ribbon edges. However, a significant decrease of oxygen-vacancy formation energies is observed on formation of <101>r edge by exfoliating (101)s slabs. Also, among the structures studied, we found <101>r edges to be the most reactive and (010)s surfaces to be the least reactive.