We introduce plans for electron-cooling of the Relativistic Heavy Ion Collider (RHIC). This project has a number of new features as electron coolers go: It will cool 100 GeV/nucleon ions with 50 MeV electrons; it will be the first attempt to cool a collider at storage-energy; and it will be the first cooler to use a bunched beam and a linear accelerator as the electron source. The linac will be superconducting with energy recovery. The electron source will be based on a photocathode gun. The project is carried out by the Collider-Accelerator Department at BNL in collaboration with the Budker Institute of Nuclear Physics.