We report a synthetic route to achieving nanoscale heterostructures consisting of a metal core and monocrystalline semiconductor shell with substantial lattice mismatches between them, which cannot be obtained by conventional epitaxial techniques. By controlling soft acid-base coordination reactions between molecular complexes and colloidal nanostructures, we show that chemical thermodynamics can drive nanoscale monocrystalline growth of the semiconductor shell with a lattice structure incommensurate with that of the core. More complex hybrid core-shell structures with azimuthal and radial nanotailoring of structures and compositions of the monocrystalline semiconductor shell are also demonstrated.