Perhaps the most ‘dangerous’ aspect of future climate change is the possibility that human activities will push parts of the climate system past tipping points, leading to irreversible impacts. The likelihood of such large-scale singular events is expected to increase with global warming^,,, but is fundamentally uncertain. A key question is how should the uncertainty surrounding tipping events^, affect climate policy? We address this using a stochastic integrated assessment model, based on the widely used deterministic DICE model. The temperature-dependent likelihood of tipping is calibrated using expert opinions, which we find to be internally consistent. The irreversible impacts of tipping events are assumed to accumulate steadily over time (rather than instantaneously^,,,), consistent with scientific understanding^,. Even with conservative assumptions about the rate and impacts of a stochastic tipping event, today’s optimal carbon tax is increased by ∼50%. For a plausibly rapid, high-impact tipping event, today’s optimal carbon tax is increased by >200%. The additional carbon tax to delay climate tipping grows at only about half the rate of the baseline carbon tax. This implies that the effective discount rate for the costs of stochastic climate tipping is much lower than the discount rate^,, for deterministic climate damages. Our results support recent suggestions that the costs of carbon emission used to inform policy^, are being underestimated^,,, and that uncertain future climate damages should be discounted at a low rate^,,,.