A systems study, including physics, engineering and costing, has been conducted to assess the feasibility of a relativistic-klystron two-beam-accelerator (RK-TBA) system as a RF power source candidate for a 1 TeV linear collider. Several key issues associated with a realizable RK-TBA system have been addressed, and corresponding schemes have been developed and examined quantitatively. A point design example has been constructed to present a concrete conceptual design which has acceptable transverse and longitudinal beam stability properties. The overall efficiency of RF production for such a power source is estimated to be 36%, and the cost of the full system is estimated to be less than 1 billion dollars