  We present a spectroscopic survey of 2046 red giant stars, distributed over
the central 4x2 kpc of the Small Magellanic Cloud (SMC). After fitting and
removing a small velocity gradient across the SMC (7.9 km/s/deg oriented at 10
deg E of N), we measure an rms velocity scatter of 27.5+-0.5 km/s. The line of
sight velocity distribution is well-characterized by a Gaussian and the
velocity dispersion profile is nearly constant as a function of radius. We find
no kinematic evidence of tidal disturbances. Without a high-precision
measurement of the SMC's proper motion, it is not possible to constrain the
SMC's true rotation speed from our measured radial-velocity gradient. However,
even with conservative assumptions, we find that v < sigma and hence that the
SMC is primarily supported by its velocity dispersion. We find that the shape
of the SMC, as measured from the analysis of the spatial distribution of its
red giant stars, is consistent with the degree of rotational flattening
expected for the range of allowed v/sigma values. As such, the properties of
the SMC are consistent with similar low luminosity spheroidal systems. We
conclude that the SMC is primarily a low luminosity spheroid whose irregular
visual appearance is dominated by recent star formation. A simple virial
analysis using the measured kinematics implies an enclosed mass within 1.6 kpc
of between 1.4 and 1.9x10^9 Mo, and a less well constrained mass within 3 kpc
of between 2.7 and 5.1x10^9 Mo.
