To fully exploit the device potential of graphene, reliable production of large-area, high-quality samples is required. Epitaxial growth on metal substrates have shown promise in this regard, but further improvement would be facilitated by a more complete understanding of the atomistic processes involved in the early growth stages. Using first-principles calculations within density functional theory, we have investigated the energetics and kinetics of graphene nucleation and growth on a Cu(111) surface. Our calculations have revealed an energetic preference for the formation of stable one-dimensional carbon nanoarches consisting of 3–13 atoms when compared to two-dimensional compact islands of equal sizes. We also estimate the critical cluster size that marks the transition from nanoarch dominance to island dominance in the growth sequence. Our findings may provide the structural link between nucleated carbon dimers and larger carbon nanodomes, and are expected to stimulate future experimental efforts.