Approximately 10 per cent of star clusters are found in pairs, known as binary clusters. We propose a mechanism for binary cluster formation; we use N-body simulations to show that velocity substructure in a single (even fairly smooth) region can cause binary clusters to form. This process is highly stochastic and it is not obvious from a regions initial conditions whether a binary will form and, if it does, which stars will end up in which cluster. We find the probability that a region will divide is mainly determined by its virial ratio, and a virial ratio above equilibrium is generally necessary for binary formation. We also find that the mass ratio of the two clusters is strongly influenced by the initial degree of spatial substructure in the region.