The quantum Hall effect(1) allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of R(K) = h/e(2) = 25 812.807 557(18) Omega, the resistance quantum(2). Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology-a few parts per billion-has been achieved only in silicon and III-V heterostructure devices(3-5). Graphene should, in principle, be an ideal material for a quantum resistance standard(6), because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels(7)) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million(8). Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.