The nucleation and growth mechanisms of graphene on Rh(111) via temperature-programmed growth of C(2)H(4) are studied by scanning tunneling microscopy and spectroscopy, and by density functional theory calculations. By combining our experimental and first-principles approaches, we show that carbon nanoislands form in the initial stages of graphene growth, possessing an exclusive size of seven honeycomb carbon units (hereafter labeled as 7C(6)). These clusters adopt a domelike hexagonal shape indicating that bonding to the substrate is localized on the peripheral C atoms. Smoluchowski ripening is identified as the dominant mechanism leading to the formation of graphene, with the size-selective carbon islands as precursors. Control experiments and calculations, whereby coronene molecules, the hydrogenated analogues of 7C(6), are deposited on Rh(111), provide an unambiguous structural and chemical identification of the 7C(6) building blocks.