The heterogeneous nature of eukaryotic replication kinetics and the low efficiency of individual initiation sites make mapping the location and timing of replication initiation in human cells difficult. To address this challenge, we have developed optical replication mapping (ORM), a high-throughput single-molecule approach, and used it to map early-initiation events in human cells. The single-molecule nature of our data and a total of > 2,500-fold coverage of the human genome on 27 million fibers averaging approximately 300 kb in length allow us to identify initiation sites and their firing probability with high confidence. We find that the distribution of human replication initiation is consistent with inefficient, stochastic activation of heterogeneously distributed potential initiation complexes enriched in accessible chromatin. These observations are consistent with stochastic models of initiation-timing regulation and suggest that stochastic regulation of replication kinetics is a fundamental feature of eukaryotic replication, conserved from yeast to humans.