A large-scale (C-13)O map (containing 33,000 spectra on a 1-arcmin grid) is presented for the giant molecular cloud located in the southern part of Ori which contains the Ori Nebula, NGC 1977, and the L1641 dark cloud complex. The overall structure of the cloud is filamentary, with individual features having a length up to 40 times their width. The northern portion of the cloud is compressed, dynamically relaxed, and supports massive star formation. In contrast, the southern part of the Ori A cloud is diffuse, exhibits chaotic spatial and velocity structure, and supports only intermediate- to low-mass star formation. This morphology may be the consequence of the formation and evolution of the Ori OB I association centered north of the molecular cloud. The entire cloud, in addition to the 5000-solar-mass filament containing both OMC-1 and OMC-2, exhibits a north-south velocity gradient. Implications of the observed cloud morphology for theories of molecular cloud evolution are discussed.