We have detected substructure within the smooth scattering disk of the celebrated Galactic Center radio source Sagittarius A* (SgrA*). 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 $theta_mathrm{d}propto lambda^2$ scaling of angular broadening $theta_mathrm{d}$ 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 SgrA*. 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.
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