The radial velocities of a total of 94 Planetary Nebulae (PN) in the Large Magellanic Cloud (LMC) have been determined. The kinematics of the population of planetary nebulae is compared with the H I data in the context of a re-analysis of the survey by Rohlfs et al. (1984), taking into account the transverse velocity of the LMC. We find that the best solution for this transverse velocity is 275±65 km s−1, and that the LMC is near perigalacticon. This is consistent with a maximum Galactic mass of order 4.5 × 1011M⊙ out to 51 kpc the rotation curve obtained after correction for this velocity implies a mass of (4.6 × 0.3) × 109 M⊙ within a radius of 3 degrees, or about 6 × 109 M⊙, total. The rotation solution for the PN population is essentially identical with that of the H I, but the vertical velocity dispersion of 19.1 km s−1 is much greater than the value of 5.4 km s−1 found for the H I. This increase in velocity dispersion is consistent with it being the result of orbital heating and diffusion operating in the LMC in a manner essentially identical with that found for the solar neighbourhood.