A bimetallic CoCu alloy thin-film catalyst is developed that enables the growth of uniform, high-quality graphene at 750 °C in 3 min by chemical vapour deposition. The growth outcome is found to vary significantly as the Cu concentration is varied, with ∼1 at% Cu added to Co yielding complete coverage single-layer graphene growth for the conditions used. The suppression of multilayer formation is attributable to Cu decoration of high reactivity sites on the Co surface which otherwise serve as preferential nucleation sites for multilayer graphene. X-ray photoemission spectroscopy shows that Co and Cu form an alloy at high temperatures, which has a drastically lower carbon solubility, as determined by using the calculated Co-Cu-C ternary phase diagram. Raman spectroscopy confirms the high quality (ID/IG < 0.05) and spatial uniformity of the single-layer graphene. The rational design of a bimetallic catalyst highlights the potential of catalyst alloying for producing two-dimensional materials with tailored properties.