Theories of free agency based on indeterminism -- that is, libertarian theories -- are often accused of undermining an agent's integrity: If an action is due to indeterministic happenings, how can it be called the agent's action to begin with? Isn't a deterministic connection between an agent's circumstances and her action needed to maintain her integrity? We claim that a meaningful notion of agency does not need determinism. In this paper we introduce stochastic libertarianism, a novel theory of free agency (...) under indeterminism. Based on a physically motivated, stochastic model of the temporal evolution of a deliberation process, stochastic libertarianism views indeterminism as a core resource for meaningful agency rather than as a threat. We counter the supposed threat by explicitly discussing Van Inwagen's replay argument, exposing a flaw in the argument that is due to insufficient attention to temporal details. Our approach can also explain how a stochastically libertarian agent developing over time can exhibit highly realiable behavior. We claim, therefore, that integrity in action does not need determinism. (shrink)