Cooperation is central to human social behaviour. However, choosing to cooperate requires individuals to incur a personal cost to benefit others. Here we explore the cognitive basis of cooperative decision-making in humans using a dual-process framework. We ask whether people are predisposed towards selfishness, behaving cooperatively only through active self-control; or whether they are intuitively cooperative, with reflection and prospective reasoning favouring 'rational' self-interest. To investigate this issue, we perform ten studies using economic games. We find that across a range of experimental designs, subjects who reach their decisions more quickly are more cooperative. Furthermore, forcing subjects to decide quickly increases contributions, whereas instructing them to reflect and forcing them to decide slowly decreases contributions. Finally, an induction that primes subjects to trust their intuitions increases contributions compared with an induction that promotes greater reflection. To explain these results, we propose that cooperation is intuitive because cooperative heuristics are developed in daily life where cooperation is typically advantageous. We then validate predictions generated by this proposed mechanism. Our results provide convergent evidence that intuition supports cooperation in social dilemmas, and that reflection can undermine these cooperative impulses.