We document large, persistent exposures of hedge funds to downside tail risk. For instance, the hardest hit hedge funds in the 1998 crisis also suffered predictably worse returns than their peers in 2007-2008. Using the conditional tail risk factor derived by Kelly (2012), we find that tail risk is a key driver of hedge fund returns in both the time-series and cross-section. A positive one standard deviation shock to tail risk is associated with a contemporaneous decline of 2.88% per year in the value of the aggregate hedge fund portfolio. In the cross-section, funds that lose value during high tail risk episodes earn average annual returns more than 6% higher than funds that are tail risk-hedged, controlling for commonly used hedge fund factors. These results are consistent with the notion that a significant component of hedge fund returns can be viewed as compensation for selling disaster insurance.