We developed the growth technique of epitaxial nanocrystals of FeGeγ (γ > 1.52), a recently-found new crystal with incommensurate Nowotny chimney-ladder phase, on Si(001) substrates. This bulk material is promising for thermoelectric application, and now their films and nanostructures are expected to be fabricated. However, it was difficult to grow single phase epitaxial FeGeγ directly on Si substrates by conventional growth method. On the other hand, we successfully formed almost single phase epitaxial FeGeγ nanocrystals on Si substrates covered with ultrathin SiO2 films with nanowindows. Reflection high energy electron diffraction indicated that the nanocrystals had the Nowotny chimney-ladder structure, the lattice constants of which were approximately consistent with those of FeGeγ bulk. This indicated strain relaxation in nanocrystals due to the hemispherical shape. This will open a road to realize high performance thermoelectric nanomaterials on Si substrates.