We have detected substructure within the smooth scattering disk of the celebrated Galactic Center radio source Sagittarius A* ( Sgr A ^ { \ast } ) . We observed this structure at 1.3 cm wavelength with the Very Long Baseline Array together with the Green Bank Telescope , on baselines of up to 3000 km , long enough to completely resolve the average scattering disk . Such structure is predicted theoretically , as a consequence of refraction by large-scale plasma fluctuations in the interstellar medium . Along with the much-studied \theta _ { d } \propto \lambda ^ { 2 } scaling of angular broadening \theta _ { d } with observing wavelength \lambda , our observations indicate that the spectrum of interstellar turbulence is shallow , with an inner scale larger than 300 km . The substructure is consistent with an intrinsic size of about 1 mas at 1.3 cm wavelength , as inferred from deconvolution of the average scattering . Further observations of the substructure can set stronger constraints on the properties of scattering material and on the intrinsic size of Sgr A ^ { \ast } . These constraints will guide understanding of effects of scatter-broadening and emission physics of the black hole , in images with the Event Horizon Telescope at millimeter wavelengths .