This paper asks whether prioritarianism – the view that social welfare orderings should give explicit priority to the worse-off – is consistent with the normative theory of equality of opportunity. We show that there are inherent tensions between some of the axioms underpinning prioritarianism and the principles underlying equality of opportunity; but also that these inconsistencies vanish under plausible adjustments to the domains of two key axioms, namely anonymity and the transfer principle. That is: reconciling prioritarianism and equality of opportunity is possible but allowing room for individual responsibility within prioritarianism requires compromises regarding the nature and scope of both impartiality and inequality aversion. The precise nature of the compromises depends on the specific variant of the theory of equality of opportunity that is adopted, and we define classes of social welfare functions and discuss relevant dominance conditions for six such variants. The conflicts and the paths to reconciliation are illustrated in an application to South Africa between 2008 and 2017, where results suggest broad empirical agreement among the different approaches.