Essentially all undoped cuprates exhibit a quasiplanar, fourfold Cu-O coordination responsible for the magnetically active antibonding 3d(x(2)-y(2)) like state. Here, we present an electronic structure study for CuSb(2)O(6) that reveals, in contrast, a half-filled 3d(3z(2)-r(2)) orbital. This hitherto unobserved ground state originates from a competition of in- and out-of-plaquette orbitals where the strong Coulomb repulsion drives the surprising and unique orbital ordering. This, in turn, gives rise to an unexpected quasi-one-dimensional magnetic behavior. Our results provide a consistent explanation of recent thermodynamical and neutron diffraction measurements.