Recent estimates of the global carbon budget, or allowable cumulative CO2 emissions consistent with a given level of climate warming, have the potential to inform climate mitigation policy discussions aimed at maintaining global temperatures below 2 °C. This raises difficult questions, however, about how best to share this carbon budget amongst nations in a way that both respects the need for a finite cap on total allowable emissions, and also addresses the fundamental disparities amongst nations with respect to their historical and potential future emissions. Here we show how the contraction and convergence (C&C) framework can be applied to the division of a global carbon budget among nations, in a manner that both maintains total emissions below a level consistent with 2 °C, and also adheres to the principle of attaining equal per capita CO2 emissions within the coming decades. We show further that historical differences in responsibility for climate warming can be quantified via a cumulative carbon debt (or credit), which represents the amount by which a given country's historical emissions have exceeded (or fallen short of) the emissions that would have been consistent with their share of world population over time. This carbon debt/credit calculation enhances the potential utility of C&C, therefore providing a simple method to frame national climate mitigation targets in a way that both accounts for historical responsibility, and also respects the principle of international equity in determining future emissions allowances.