This paper estimates that the macroeconomic damages from climate change are six times larger than previously thought. We exploit natural variability in global temperature and rely on time- series variation. A 1°C increase in global temperature leads to a 12% decline in world GDP. Global temperature shocks correlate much more strongly with extreme climatic events than the country-level temperature shocks commonly used in the panel literature, explaining why our estimate is substantially larger. We use our reduced-form evidence to estimate structural damage functions in a standard neoclassical growth model. Our results imply a Social Cost of Carbon of $1,056 per ton of carbon dioxide. A business-as-usual warming scenario leads to a present value welfare loss of 31%. Both are multiple orders of magnitude above previous estimates and imply that unilateral decarbonization policy is cost-effective for large countries such as the United States.