We investigate whether investors receive compensation for holding stocks with strong systematic liquidity risk in the form of extreme downside liquidity (EDL) risk. Following the logic of Acharya and Pedersen (2005), we capture a stock's EDL risk by the lower tail dependence between (i) individual stock liquidity and market liquidity, (ii) individual stock return and market liquidity, and (iii) individual stock liquidity and the market return. We show that the cross-section of expected stock returns reflects a premium for EDL risk. From 1969 to 2011, the average future return on stocks with strong EDL risk exceeds that of stocks with weak EDL risk by more than 4% annually, adjusted for the exposures to market return as well as size, value, and momentum. This premium is different from linear liquidity risk and cannot be explained by other firm characteristics and risk factors. Our results show that investors care about extreme joint realizations in liquidity and that asset pricing models that rely on linear sensitivities alone might be misspecified.