Limits on the Position Wander of Sgr A*

We present measurements with the VLBA of the variability in the centroid position of Sgr A* relative to a background quasar at 7-mm wavelength. We find an average centroid wander of 71 +/- 45 micro-arcsec for time scales between 50 and 100 min and 113 +/- 50 micro-arcsec for timescales between 100 and 200 min, with no secular trend. These are sufficient to begin constraining the viability of the hot-spot model for the radio variability of Sgr A*. It is possible to rule out hot spots with orbital radii above 15GM_SgrA*/c^2 that contribute more than 30% of the total 7-mm flux. However, closer or less luminous hot spots remain unconstrained. Since the fractional variability of Sgr A* during our observations was ~20% on time scales of hours, the hot-spot model for Sgr A*'s radio variability remains consistent with these limits. Improved monitoring of Sgr A*'s centroid position has the potential to place significant constraints upon the existence and morphology of inhomogeneities in a supermassive black hole accretion flow.