The rotation of the disk of the Large Magellanic Cloud ( LMC ) is derived from the radial velocities of 422 carbon stars ( Kunkel , Irwin , & Demers 1997 , A & AS , 122 , 463 ) . 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 LMC rotation curve reaches a maximum circular velocity of 72 \pm 7 km s ^ { -1 } at R = 4.0 kpc and then declines . The rotation curve is well fit by a truncated , finite-thickness exponential disk model with no dark halo , implying a total mass of 5.3 \pm 1.0 \times 10 ^ { 9 } M _ { \odot } . The velocity dispersion in concentric radial bins from R = 0.5 to 5.6 kpc decreases from 22 to 15 km s ^ { -1 } , then increases to \sim 20 km s ^ { -1 } at larger radii . Constant-thickness disk models in virial equilibrium can not be reconciled with the data even if the effects of LMC or Galactic dark halos are included . If the disk is virialized , the scale height rises from h = 0.3 to 1.6 kpc over the range of R = 0.5 to 5.6 kpc . Thus 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 \overline { \rho } \sim 2.5 \times 10 ^ { -4 } M _ { \odot } 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 . The instantaneous probability of microlensing from LMC stars in our model is \tau < 1.0 \times 10 ^ { -8 } \cdot { sec } ^ { 2 } i , where i is the disk inclination . 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 .