This paper examines the socially optimal pricing of carbon emissions over time when climate-change impacts are unknown, potentially high-consequence events. The carbon price tends to increase with income. But learning about impacts, or their absence, decouples the carbon price from income growth. The price should grow faster than the economy if the past warming is not substantial enough for learning the true long-run social cost. It grows slower than the economy as soon as the warming generates information about events that could have arrived but have not done so. A quantitative assessment shows that the price grows roughly at the rate of the economy for the next 100 years.