In this paper we present a simple model for assessing the willingness to pay for reductions in the risk associated with catastrophic climate change. The model is extremely tractable and applies to a multiregion world but with global externalities and has five key features: (i) Neither the occurrence nor the costs of a catastrophic event in any one year are precisely predictable; (ii) the probability of a catastrophe occurring in any one year increases as the levels of greenhouse gases in the atmosphere increase; (iii) greenhouse gases are a worldwide public bad with emissions from any one country or region increasing the risks for all; (iv) there is two-sided irreversibility; if nothing is done and the problem proves serious, the climate, economic activity, and human life will suffer permanent damage, but if we spend large sums on countermeasures and the problem turns out to be minor or even nonexistent, we will have wasted resources unnecessarily; and (v) technological progress may yield partial or even complete solutions. The framework that we propose can give a sense of the quantitative significance of mitigation strategies. We illustrate these for a core set of parameter values.