Motivated by extensive evidence that stock-return correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) may be priced. Wepropose a direct and intuitive test by comparing option-implied correlations between stock returns (obtained by combining index option prices with prices of options on all index components)with realized correlations. Our parsimonious model shows that the substantial gap between average implied (39.5% for S&P500 and 46.0% for DJ30) and realized correlations (32.5% and 35.5%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that option-impliedcorrelations have remarkable predictive power for future stock market returns, which also stays significant after controlling for a number of fundamental market return predictors.