Thomas Piketty's "Capital in the Twenty-First Century" is best known for its documentation of increasing social inequality, but it also has a notable normative aspect. Although Piketty is far less clear on the normative level than on the empirical, his view of justice can be summarised as meritocratic luck egalitarianism. This leads him to condemn as unjust the fact that inheritance is once again becoming more important than education for determining social position. In this paper, I discuss whether Piketty's normative conception can justify this condemnation. My main thesis will be that Piketty ends up in a dilemma that he cannot resolve with the normative resources he has at his disposal. The horns of this dilemma are defined by whether or not we accept what Susan Hurley calls "the regression requirement", and in both cases the normative distinction between inheritance and education as ways to achieve social positions disappears. Toward the end, I shall suggest an alternative justification for the moral superiority of education over inheritance, which makes use of one of Piketty's key empirical arguments.