  The rotation of the disk of the Large Magellanic Cloud (LMC) is derived from
the radial velocities of 422 carbon stars. New aspects of this analysis include
the propagation of uncertainties in the LMC proper motion with a Monte Carlo,
and a self-consistent modeling of the rotation curve and disk kinematics. The
rotation curve is well fit by a truncated, finite-thickness exponential disk
model with no dark halo. The velocity dispersion in radial bins decreases from
22 to 15 km/s, then increases to 20 km/s at larger radii. Constant-thickness
models in virial equilibrium cannot be reconciled with the data even if the
effects of LMC or Galactic dark halos are included. If the disk is virialized,
the LMC disk is flared. We model the velocity dispersion at large radii (R > 6
kpc) as a maximal flared disk under the influence of the Galactic dark halo,
which favors a mean density for the latter of 0.00025 M_sol/pc^3 at the LMC
distance. LMC stellar kinematics play an important role in elucidating the
nature of MACHOs, a dark population inferred from LMC microlensing. We have
constructed a truncated and flared maximal disk model for the LMC which is
kinematically based. Our model does not include a nonvirialized component such
as tidal debris. Our upper limit on the self-lensing optical depth is in good
agreement with that obtained from less sophisticated models, and is an order of
magnitude too small to account for the MACHO microlensing signal [Abridged].
