We have demonstrated a storage ring for ultracold neutral atoms. Atoms with mean velocities of 1 m/s corresponding to kinetic energies of approximately 100 neV are confined to a 2 cm diameter ring by magnetic forces produced by two current-carrying wires. Up to 10(6) atoms are loaded at a time in the ring, and seven revolutions are clearly observed. Additionally, we have demonstrated multiple loading of the ring and deterministic manipulation of the longitudinal velocity distribution of the atoms using applied laser pulses. Applications of this ring include large area atom interferometers and monochromatic atomic beam generation.