We mapped the NGC 1333 section of the Perseus Molecular Cloud in the J=2-1 emission lines of ^12^CO and ^13^CO over a 50'x60' region (3.4x4.1pc at the cloud distance of 235pc), using the Arizona Radio Observatory Heinrich Hertz Submillimeter Telescope. The angular resolution is 38" (0.04pc) and velocity resolution is 0.3km/s. We compare our velocity moment maps with known positions of young stellar objects (YSOs) and (sub)millimeter dust continuum emission. The CO emission is brightest at the center of the cluster of YSOs, but is detected over the full extent of the mapped region at >=10xrms. The morphology of the CO channel maps shows a kinematically complex structure, with many elongated features extending from the YSO cluster outward by ~1pc. One notable feature appears as a narrow serpentine structure that curves and doubles back, with a total length of ~3pc. The ^13^CO velocity channel maps show evidence for many low-density cavities surrounded by partial shell-like structures, consistent with previous studies. Maps of the velocity moments show localized effects of bipolar outflows from embedded YSOs, as well as a large-scale velocity gradient around the central core of YSOs, suggestive of large-scale turbulent cloud motions determining the location of current star formation. The CO/^13^CO intensity ratios show the distribution of the CO opacity, which exhibits a complex kinematic structure. Identified YSOs are located mainly at the positions of greatest CO opacity.