  Polarization-dependent phase-contrast imaging is used to spatially resolve
the magnetization of an optically trapped ultracold gas. This probe is applied
to Larmor precession of degenerate and nondegenerate spin-1 $^{87}$Rb gases.
Transverse magnetization of the Bose-Einstein condensate persists for the
condensate lifetime, with a spatial response to magnetic field inhomogeneities
consistent with a mean-field model of interactions. Rotational symmetry implies
that the Larmor frequency of a spinor condensate be density-independent, and
thus suitable for precise magnetometry with high spatial resolution. In
comparison, the magnetization of the noncondensed gas decoheres rapidly.
