Eukaryotic chromosomes replicate with defined timing patterns. However, the mechanism that regulates the timing of replication is unknown. In particular, there is an apparent conflict between population experiments, which show defined average replication times, and single-molecule experiments, which show that origins fire stochastically. Here, we provide a simple simulation that demonstrates that stochastic origin firing can produce defined average patterns of replication firing if two criteria are met. The first is that origins must have different relative firing probabilities, with origins that have relatively high firing probability being likely to fire in early S phase and origins with relatively low firing probability being unlikely to fire in early S phase. The second is that the firing probability of all origins must increase during S phase to ensure that origins with relatively low firing probability, which are unlikely to fire in early S phase, become likely to fire in late S phase. In addition, we propose biochemically plausible mechanisms for these criteria and point out how stochastic and defined origin firing can be experimentally distinguished in population experiments.