CO observations of the peculiar galaxy M82 have been made at 79 positions using the 14 m FCRAO telescope (HPBW = 50'') in order to obtain a fully sampled map of the central 2 kpc as well as the radial distribution of molecular gas out to 3 kpc along the major axis. These data comprise the highest resolution kinematic information yet determined for M82 extending over the entire optical disk of the galaxy. The velocity field of the molecular gas exhibits peculiarities, suggesting noncircular velocities of 50 km s/sup -1/ at positions 1'.5 from the center between the major and minor axis. We suggest that the systemic velocity of M82 is close to a value of 175 km s/sup -1/, a conclusion which is supported not only by the CO data, but also by some previous optical and infrared observations. Contrary to recent assertions about anomalous minor axis emission, then, the CO emission seen on the minor axis with velocities near 170 km s/sup -1/ is precisely what one would expect for a rotating disk.