At radio wavelengths, images of the compact radio source Sagittarius A* (Sg
r A*) in the Galactic center are scatter broadened with a lambda (2) depend
ence due to an intervening ionized medium. We present VLBI observations of
Sgr A* at 86 GHz using a six station array, including the VLBA antennas at
Pie Town, Fort Davis, and Los Alamos, the 12 m antenna at Kitt Peak, and th
e millimeter arrays at Hat Creek and Owens Valley. To avoid systematic erro
rs due to imperfect antenna calibration, the data were modeled using interf
erometric closure information. The data are best modeled by a circular Gaus
sian brightness distribution of FWHM 0.18 +/- 0.02 mas. The data are also s
hown to be consistent with an elliptical model corresponding to the scatter
ing of a point source. The source structure in the north-south direction, w
hich is less well determined than in the east-west direction because of the
limited north-south u-v coverage of the array, is constrained to be less t
han 0.27 mas by these measurements. These results are consistent with extra
polations of intrinsic structure estimates obtained with VLBI at a 7 mm wav
elength, assuming the intrinsic size of Sgr A* has a greater dependence tha
n lambda (0.9) with wavelength.