  Using the Submillimeter Array, we have made the first high angular resolution
measurements of the linear polarization of Sagittarius A* at submillimeter
wavelengths, and the first detection of intra-day variability in its linear
polarization. We detected linear polarization at 340 GHz (880um) at several
epochs. At the typical resolution of 1.4"x2.2", the expected contamination from
the surrounding (partially polarized) dust emission is negligible. We found
that both the polarization fraction and position angle are variable, with the
polarization fraction dropping from 8.5% to 2.3% over three days. This is the
first significant measurement of variability in the linear polarization
fraction in this source. We also found variability in the polarization and
total intensity within single nights, although the relationship between the two
is not clear from these data. The simultaneous 332 and 342 GHz position angles
are the same, setting a one-sigma rotation measure (RM) upper limit of 7x10^5
rad/m^2. From position angle variations and comparison of "quiescent" position
angles observed here and at 230 GHz we infer that the RM is a few times 10^5
rad/m^2, a factor of a few below our direct detection limit. A generalized
model of the RM produced in the accretion flow suggests that the accretion rate
at small radii must be low, below 10^{-6} to 10^{-7} M_{sun}/year depending on
the radial density and temperature profiles, but in all cases below the gas
capture rate inferred from X-ray observations.
