We report imaging of CO (2-1) emission in the nucleus of M51 at 1'' (47 pc) resolution. Molecular gas is found closely associated with the nuclear radio jet and the X-shaped dust absorption feature seen in the Hubble Space Telescope images. The CO emission lies along the side of the nuclear radio continuum "jet." The strongest molecular emission is not symmetric in either position or velocity with respect to the nucleus—the dominant feature is at redshifted velocities and peaks 1'' to the west of the radio/optical nucleus. The CO (2-1) emission has an integrated flux implying a molecular gas mass of 10⁷ M for a standard Galactic giant molecular cloud CO-to-H₂ conversion ratio, which is consistent with the total virial mass of the individual complexes. The redshifted CO emission is elongated with a deconvolved semimajor axis of 65 pc (138). Assuming the molecular gas moves in circular orbit about the nucleus (defined by the point radio source), we find a dynamical mass of 2 × 10⁸ M at R≥47 pc with no correction for inclination. The molecular gas has sufficient density (≥10⁵ cm^-3) to collimate the radio jet and ionized outflow from the active galactic nucleus (AGN), and this gas may in fact be the reservoir of matter that supplies the AGN.