The Primary Atomic Reference Clock in Space (PARCS) mission is designed to perform certain tests of relativity theory, to study the performance of individual GPS space-vehicle clocks, to study the dynamics of atom motion in microgravity, to advance the state-of-the art for space clocks, and to serve as a pathfinder for precision instruments based on laser cooling of atoms. After a brief overview of the project, this paper discusses the specific objectives of PARCS, describes the key subsystems, and discusses the systematic frequency shifts that limit the accuracy of the clock.