At radio wavelengths, images of the compact radio source Sagittarius A* (Sgr A*) in the Galactic Center are scatter broadened with a lambda 2 dependence 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 the millimeter arrays at Hat Creek and Owens Valley. To avoid systematic errors due to imperfect antenna calibration, the data were modeled using interferometric closure information. The data are best modeled by a circular Gaussian brightness distribution of FWHM 0.18 +/- 0.02 mas. The data are also shown to be consistent with an elliptical model corresponding to the scattering of a point source. The source structure in the N-S direction, which is less well determined than in the E-W direction due to the limited N-S (u,v) coverage of the array, is constrained to be less than 0.27 mas by these measurements. These results are consistent with extrapolations of intrinsic structure estimates obtained with VLBI at 7 mm wavelength assuming the intrinsic size of Sgr A* has a greater dependence than lambda 0.9 with wavelength.