DNA replication initiates at discrete origins along eukaryotic chromosomes. However, in most organisms, origin firing is not efficient; a specific origin will fire in some but not all cell cycles. This observation raises the question of how individual origins are selected to fire and whether origin firing is globally coordinated to ensure an even distribution of replication initiation across the genome. We have addressed these questions by determining the location of firing origins on individual fission yeast DNA molecules using DNA combing. We show that the firing of replication origins is stochastic, leading to a random distribution of replication initiation. Furthermore, origin firing is independent between cell cycles; there is no epigenetic mechanism causing an origin that fires in one cell cycle to preferentially fire in the next. Thus, the fission yeast strategy for the initiation of replication is different from models of eukaryotic replication that propose coordinated origin firing.