Shape symmetry breaking in the formation of inorganic nanostructures is of significant current interest. It was typically achieved through the growth of colloidal nanoparticles with adsorbed chiral molecules. Photochemical processes induced through asymmetric plasmon excitation by circularly polarized light in surface immobilized nanostructures also led to symmetry breaking. Here, we show that chiral symmetry breaking can be achieved by randomly rotating gold@silver core-shell nanobars in colloidal solution using circularly polarized illumination, where orientational averaging does not eliminate the symmetry breaking of an asymmetric plasmon-induced galvanic replacement reaction. Different morphological effects that are produced by circularly vs linearly polarized light illumination demonstrate the intricate effect of light polarization on the localized plasmonic-induced photochemical response. The essential features of this symmetry breaking, such as illumination wavelength dependence, were reproduced by simulations of circularly polarized light-excited-plasmon-induced hot-electron generation as the source for asymmetric metal deposition. The symmetry breaking becomes smaller in more symmetric geometrical shapes, such as triangular nanoprisms and nanocubes, and down to zero in spherical ones. The degree of symmetry breaking rises when the nanobars are immobilized on a substrate and illuminated from a single direction.