We present 7 mm lambda VLBA observations of the compact nonthermal radio source in the Galactic Center, Sgr A*. These observations confirm the hypothesis that the image of Sgr A* is a resolved elliptical Gaussian caused by the scattering of an intervening thermal plasma. The measured major axis of Sgr A* is 0.76 +/- 0.04 mas, consistent with the predicted scattering size of 0.67 +/- 0.03. We find an axial ratio of 0.73 +/- 0.10 and a position angle of 77o +/- 7o. These results are fully consistent with VLBI observations at longer wavelengths and at 3 mm lambda . We find no evidence for any additional compact structure to a limit of 35 mJy. The underlying radio source must be smaller than 4.1 AU for a galactocentric distance of 8.5 kpc. This result is consistent with the conclusion that the radio emission from Sgr A* results from synchrotron or cyclo-synchrotron radiation of gas in the vicinity of a black hole with a mass near 10^6 Mo.