Coherent electron cooling (CEC) has a potential to significantly boost luminosity of high-energy, high-intensity hadron-hadron and electron-hadron colliders. In a CEC system, a hadron beam interacts with a cooling electron beam. A perturbation of the electron density caused by ions is amplified and fed back to the ions to reduce the energy spread and the emittance of the ion beam. To demonstrate the feasibility of CEC we propose a proof-of-principle experiment at RHIC using SRF linac. In this paper, we describe the setup for CeC installed into one of RHIC's interaction regions. We present results of analytical estimates and results of initial simulations of cooling a gold-ion beam at 40 GeV/u energy via CeC. We plan to complete the program in five years. During first two years we will build coherent electron cooler in IP2 of RHIC. In parallel we will develop complete package of computer simulation tools for the start-to-end simulation predicting exact performance of a CeC. The later activity will be the core of Tech X involvement into the project. We will use these tools to predict the performance of our CeC device. The experimental demonstration of the CeC will be undertaken in years three to five of …