A basic intuition is that arbitrage is easier when markets are most liquid. Surprisingly, we find that momentum profits are markedly larger in liquid market states. This finding is not explained by variation in liquidity risk, time-varying exposure to risk factors, or changes in macroeconomic condition, cross-sectional return dispersion, and investor sentiment. The predictive performance of aggregate market illiquidity for momentum profits uniformly exceed that of market return and market volatility states. While momentum strategies are unconditionally unprofitable in US, Japan, and Eurozone countries in the last decade, they are substantial following liquid market states.