A strain-relieved, dislocation-free InxGa1-xAs layer is selectively grown on nanoscale SiO2-patterned GaAs(001) by molecular beam epitaxy. By localizing the epitaxial area to a periodic array of nanoscale circular holes opened in a SiO2 mask and allowing the InxGa1-xAs epilayers selectively grown on adjacent holes to coalesce over the SiO2 mask by lateral overgrowth, the strain of the resulting InxGa1-xAs layer (x=0.06) is relieved with a dramatically decreased generation of misfit dislocations. These experimental results qualitatively support the basic idea of the Luryi-Suhir proposal [Appl. Phys. Lett. 49, 140 (1986)].