In an earlier paper we have demonstrated the existence of a ring of molecular hydrogen-line emission surrounding the nucleus of the Galaxy. Here we present the first detailed maps of the surface brightness and the velocity field, made in the v=1-0 5(1) line of molecular hydrogen with a spatial resolution of 18 arcsec and a velocity resolution of 130 km s-1. We find that the molecular ring is tilted approximately 20° out of the plane of the Galaxy, has a broken and clumpy appearance, rotates at 100 km s-1 in the sense of galactic rotation, and exhibits radial motion at a velocity of 50 km s-1. We interpret the radial motion as infall. Our earlier model, in which the molecular ring is created and excited by a single central engine, possibly a black hole, remains viable, and is further sup- ported and refined by the present observations.