We report progress on the R&D program for electroncooling of the Relativistic Heavy Ion Collider (RHIC). This electron cooler is designed to cool 100 GeV/nucleon at storage energy using 54 MeV electrons. The electron source will be a superconducting RF photocathode gun. The accelerator will be a superconducting energy recovery linac. The frequency of the accelerator is set at 703.75 MHz. The maximum electron bunch frequency is 9.38 MHz, with bunch charge of 20 nC. The R&D program has the following components: The photoinjector and its photocathode, the superconducting linac cavity, start-to-end beam dynamics with magnetized electrons, electron cooling calculations including benchmarking experiments and development of a large superconducting solenoid. The photoinjector and linac cavity are being incorporated into an energy recovery linac aimed at demonstrating ampere class current at about 20 MeV.