Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are directly linked to their structural boundary conditions. Nanostructures with zigzag edges are expected to host spin-polarized electronic edge states and can thus serve as key elements for graphene-based spintronics. The edge states of zigzag graphene nanoribbons (ZGNRs) are predicted to couple ferromagnetically along the edge and antiferromagnetically between the edges, but direct observation of spin-polarized edge states for zigzag edge topologies--including ZGNRs--has not yet been achieved owing to the limited precision of current top-down approaches. Here we describe the bottom-up synthesis of ZGNRs through surface-assisted polymerization and cyclodehydrogenation of specifically designed precursor monomers to yield atomically precise zigzag edges. Using scanning tunnelling spectroscopy we show the existence of edge-localized states with large energy splittings. We expect that the availability of ZGNRs will enable the characterization of their predicted spin-related properties, such as spin confinement and filtering, and will ultimately add the spin degree of freedom to graphene-based circuitry.