  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.
