Stochastic origin activation gives rise to significant cell-to-cell variability in the pattern of genome replication. The molecular basis for heterogeneity in efficiency and timing of individual origins is a long-standing question. Here, we developed Methylation Accessibility of TArgeted Chromatin domain Sequencing (MATAC-Seq) to determine single-molecule chromatin accessibility of four specific genomic loci. MATAC-Seq relies on preferential modification of accessible DNA by methyltransferases combined with Nanopore-Sequencing for direct readout of methylated DNA-bases. Applying MATAC-Seq to selected early-efficient and late-inefficient yeast replication origins revealed large heterogeneity of chromatin states. Disruption of INO80 or ISW2 chromatin remodeling complexes leads to changes at individual nucleosomal positions that correlate with changes in their replication efficiency. We found a chromatin state with an accessible nucleosome-free region in combination with well-positioned +1 and +2 nucleosomes as a strong predictor for efficient origin activation. Thus, MATAC-Seq identifies the large spectrum of alternative chromatin states that co-exist on a given locus previously masked in population-based experiments and provides a mechanistic basis for origin activation heterogeneity during eukaryotic DNA replication. Consequently, our single-molecule chromatin accessibility assay will be ideal to define single-molecule heterogeneity across many fundamental biological processes such as transcription, replication, or DNA repair in vitro and ex vivo.