This paper presents an 8 GeV Rapid Cycling Synchrotron (RCS) option for Project X. It has several advantages over an 8 GeV SC linac. In particular, the cost could be lower. With a 2 GeV 10 mA pulsed linac as injector, the RCS would be able to deliver 4 MW beam power for a muon collider. If, instead, a 2 GeV 1 mA CW linac is used, the RCS would still be able to meet the Project X requirements but it would be difficult for it to serve a muon collider due to the very long injection time.
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