We introduce the R&D program for electron-cooling of the Relativistic Heavy Ion Collider. This electron cooler is designed to cool 100GeV/nucleon bunched-beam ion collider at storage energy using 54MeV electrons. The electron source will be an RF photocathode gun. The accelerator will be a superconducting energy recovery linac. The frequency of the accelerator is set at 703.75MHz.The maximum bunch frequency is 28.15MHz, with bunch charge of 10nC. The R&D program has the following components: The photoinjector, the superconducting linac, start-to-end beam dynamics with magnetized electrons, electron-cooling calculations and development of a large superconducting solenoid.