We present 45"-47" angular resolution maps at 50" sampling of the 12CO and 13CO J = 1-0 emission toward a 1°.39x1°.33 region in the W51 H II region complex. These data permit the spatial and kinematic separation of several spectral features observed along the line of sight to W51 and establish the presence of a massive (1.2x106M☉), large (ΔlxΔb = 83x114 pc) giant molecular cloud (GMC), defined as the W51 GMC and centered at (l, b, V)c ~ (49°.5, -0°.2, 61 km.s–1). A second massive (1.9x105M☉), elongated (22x136 pc) molecular cloud is found at velocities of ∼68 km.s–1 along the southern edge of the W51 GMC. Of the five radio continuum sources that classically define the W51 region, the brightest source at λ6 cm (G49.5-0.4) is spatially and kinematically coincident with the W51 GMC and three (G48.9-0.3, G49.1-0.4, and G49.2-0.4) are associated with the 68 km.s–1 cloud. Published absorption-line spectra indicate that the fifth prominent continuum source (G49.4-0.3) is located behind the W51 molecular cloud. The W51 GMC is among the upper 1% of clouds in the Galactic disk by size and the upper 5%-10% by mass. While the W51 GMC is larger and more massive than any nearby molecular cloud, the average H2 column density is not unusual given its size, and the mean H2 volume density is comparable to that in nearby clouds. The W51 GMC is also similar to other clouds in that most of the molecular mass is contained in a diffuse envelope that is not currently forming massive stars. We speculate that much of the massive star formation activity in this region has resulted from a collision between the 68 km.s–1 cloud and the W51 GMC.