Catalytic synthesis of graphene occurs when methane reacts with cubic SiC nanopowder at 1000-1200K. The composite, created under relatively mild experimental conditions, consists primarily of 30-40 nm diameter cylinders with aspect ratios near unity whose walls are composed of 10-20 layers of graphene surrounding nano-SiC particles. Sputtering by electron irradiation sequentially removes the graphene shells thus exposing the SiC cores. Electron as well as X-ray diffraction studies reveal the highly crystalline nature of the graphene shells which constitute 90 mol% of the composites. Raman data support a model involving growth of graphene on carbon rather than on silicon terminated SiC.