Graphene has a range of unique physical properties and could be of use in the development of a variety of electronic, photonic and photovoltaic devices. For most applications, large-area high-quality graphene films are required and chemical vapour deposition (CVD) synthesis of graphene on copper surfaces has been of particular interest due to its simplicity and cost effectiveness. However, the rates of growth for graphene by CVD on copper are less than 0.4 μm s-1, and therefore the synthesis of large, single-crystal graphene domains takes at least a few hours. Here, we show that single-crystal graphene can be grown on copper foils with a growth rate of 60 μm s-1. Our high growth rate is achieved by placing the copper foil above an oxide substrate with a gap of ∼15 μm between them. The oxide substrate provides a continuous supply of oxygen to the surface of the copper catalyst during the CVD growth, which significantly lowers the energy barrier to the decomposition of the carbon feedstock and increases the growth rate. With this approach, we are able to grow single-crystal graphene domains with a lateral size of 0.3 mm in just 5 s.