We demonstrate a new kind of form birefringence in lithium niobium silicate glass induced by femtosecond laser direct writing. By combining electron backscatter diffraction and transmission electron microscopy, we reveal a self-assembled nanostructure consisting of periodic phase change: nonlinear optical nanocrystals embedded in a network of "walls" in a vitreous phase. These "walls" are aligned perpendicular to the laser polarization direction. This self-organized nanostructure may successfully explain the origin of the laser-induced birefringence in this multicomponent glass quite differently from pure silica. These findings highlight a spectacular modification of glass, and enable construction of a high contrast three-dimensional refractive index and birefringent structures at the micrometer scale in multicomponent glasses.