A liberal egalitarian theory of justice seeks to combine the values of equality, personal freedom, and personal responsibility. It is considered a much more promising position than strict egalitarianism, because it supposedly provides a fairness argument for inequalities reflecting differences in choice. However, we show that it is inherently difficult to fulfill this ambition. We present a liberal egalitarian paradox which shows that there does not exist any robust reward system that satisfies a minimal egalitarian and a minimal liberal requirement. (...) Moreover, we demonstrate how libertarianism may be justified in this framework if we drop the egalitarian condition. (shrink)