A single-layer graphene has been uniformly grown on a Cu surface at elevated temperatures by thermal processing of a poly(methyl methacrylate) (PMMA) film in a rapid thermal annealing (RTA) system under vacuum. The detailed chemistry of the transition from solid-state carbon to graphene on the catalytic Cu surface was investigated by performing in situ residual gas analysis while PMMA/Cu-foil samples were being heated, in conjunction with interrupted growth studies to reconstruct ex situ the heating process. The data clearly show that the formation of graphene occurs by vaporizing hydrocarbon molecules from PMMA, such as methane and/or methyl radicals, which act as precursors, rather than by the direct graphitization of solid-state carbon. We also found that the temperature for vaporizing hydrocarbon molecules from PMMA and the length of time the gaseous hydrocarbon atmosphere is maintained, which are dependent on both the heating temperature profile and the amount of a solid carbon feedstock, are the dominant factors that determine the crystalline quality of the resulting graphene film. Under optimal growth conditions, the PMMA-derived graphene was found to have a carrier (hole) mobility as high as ∼2700 cm(2) V(-1) s(-1) at room temperature, which is superior to common graphene converted from solid carbon.