  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 \pm 0.04 mas, consistent with the predicted scattering size of 0.67
\pm 0.03. We find an axial ratio of 0.73 \pm 0.10 and a position angle of 77.0
\pm 7.4 deg. 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 M_sun.
