We report the synthesis and crystal structure of a new high-temperature form of Ca3P2. The crystal structure was determined through Rietveld refinements of synchrotron powder x-ray diffraction data. This form of Ca3P2 has a crystal structure of the hexagonal Mn5Si3 type, with a Ca ion deficiency compared to the ideal 5:3 stoichiometry. This yields a stable, charge-balanced compound of Ca2+ and P3−. We also report the observation of a secondary hydride phase, Ca5P3H, which again is a charge-balanced compound. The calculated band structure of Ca3P2 indicates that it is a three-dimensional Dirac semimetal with a highly unusual ring of Dirac nodes at the Fermi level. The Dirac states are protected against gap opening by a mirror plane in a manner analogous to what is seen for graphene.