We have used the Submillimeter Wave Astronomy Satellite to map the ground-state 110 → 101 transition of ortho-H2O at 557 GHz in the Orion molecular cloud. H2O emission was detected in Orion over an angular extent of about 20', or nearly 3 pc. The water emission is relatively weak, with line widths (3-6 km s-1) and VLSR velocities (9-11 km s-1) consistent with an origin in the cold gas of the molecular ridge. We find that the ortho-H2O abundance relative to H2 in the extended gas in Orion varies between 1 and 8 × 10-8, with an average of 3 × 10-8. The absence of detectable narrow-line ortho-H218O emission is used to set a 3 σ upper limit on the relative ortho-H2O abundance of 7 × 10-8.