Three claims about love and justice cannot be simultaneously true and therefore entail a paradox: (1) Love is a matter of justice. (2) There cannot be a duty to love. (3) All matters of justice are matters of duty. The first claim is more controversial. To defend it, I show why the extent to which we enjoy the good of love is relevant to distributive justice. To defend (2) I explain the empirical, conceptual and axiological arguments in its favour. Although (...) (3) is the most generally endorsed claim of the three, I conclude we should reject it in order to avoid the paradox. (shrink)