We report observations of molecular oxygen (O-2) rotational transitions at 487 GHz, 774 GHz, and 1121 GHz toward Orion Peak A. The O-2 lines at 487 GHz and 774 GHz are detected at velocities of 10-12 km s(-1) with line widths similar to 3 km s(-1); however, the transition at 1121 GHz is not detected. The observed line characteristics, combined with the results of earlier observations, suggest that the region responsible for the O-2 emission is similar or equal to 9" (6 x 10(16) cm) in size, and is located close to the H-2 Peak 1 position (where vibrationally excited H-2 emission peaks), and not at Peak A, 23" away. The peak O-2 column density is similar to 1.1 x 10(18) cm(-2). The line velocity is close to that of the 621 GHz water maser emission found in this portion of the Orion Molecular Cloud, and having a shock with velocity vector lying nearly in the plane of the sky is consistent with producing maximum maser gain along the line of sight. The enhanced O-2 abundance compared to that generally found in dense interstellar clouds can be explained by passage of a low-velocity C shock through a clump with preshock density 2 x 10(4) cm(-3), if a reasonable flux of UV radiation is present. The postshock O-2 can explain the emission from the source if its line-of-sight dimension is similar or equal to 10 times larger than its size on the plane of the sky. The special geometry and conditions required may explain why O-2 emission has not been detected in the cores of other massive star-forming molecular clouds.