  We report the discovery of variability in the linear polarization from the
Galactic Center black hole source, Sagittarius A*. New polarimetry obtained
with the Berkeley-Illinois-Maryland Association array at a wavelength of 1.3 mm
shows a position angle that differs by 28 +/- 5 degrees from observations 6
months prior and then remains stable for 15 months. This difference may be due
to a change in the source emission region on a scale of 10 Schwarzschild radii
or due to a change of 3 x 10^5 rad m^-2 in the rotation measure. We consider a
change in the source physics unlikely, however, since we see no corresponding
change in the total intensity or polarized intensity fraction. On the other
hand, turbulence in the accretion region at a radius ~ 10 to 1000 R_s could
readily account for the magnitude and time scale of the position angle change.
