Genome replication mapping methods profile cell populations, masking cell-to-cell heterogeneity. Here, we describe FORK-seq, a nanopore sequencing method to map replication of single DNA molecules at 200-nucleotide resolution. By quantifying BrdU incorporation along pulse-chased replication intermediates from Saccharomyces cerevisiae, we orient 58,651 replication tracks reproducing population-based replication directionality profiles and map 4964 and 4485 individual initiation and termination events, respectively. Although most events cluster at known origins and fork merging zones, 9% and 18% of initiation and termination events, respectively, occur at many locations previously missed. Thus, FORK-seq reveals the full extent of cell-to-cell heterogeneity in DNA replication.