Abstract: An international collaboration has undertaken a project to search for the electric dipole moment (EDM) of the neutron with a sensitivity of 10**-28 e*cm.  The search should span a region of sensitivity where effects are expected from supersysmmetric models and from models of time reversal violation that might explain electroweak baryogenesis.  The technique utilizes the special properties for producing and storing ultracold neutrons in a bottle filled with liquid 4He  and doped with a small amount of 3He.  The technique will be discussed and compared to that of competing experiments.  The extensive R&D program undertaken by the collaboration will be reviewed.  The status of the DOE project will be explained.