Faithful transmission of genetic material to daughter cells involves a characteristic temporal order of DNA replication, which may play a significant role in the inheritance of epigenetic states. We developed a genome-scale approach--Repli Seq--to map temporally ordered replicating DNA using massively parallel sequencing and applied it to study regional variation in human DNA replication time across multiple human cell types. The method requires as few as 8,000 cytometry-fractionated cells for a single analysis, and provides high-resolution DNA replication patterns with respect to both cell-cycle time and genomic position. We find that different cell types exhibit characteristic replication signatures that reveal striking plasticity in regional replication time patterns covering at least 50% of the human genome. We also identified autosomal regions with marked biphasic replication timing that include known regions of monoallelic expression as well as many previously uncharacterized domains. Comparison with high-resolution genome-wide profiles of DNaseI sensitivity revealed that DNA replication typically initiates within foci of accessible chromatin comprising clustered DNaseI hypersensitive sites, and that replication time is better correlated with chromatin accessibility than with gene expression. The data collectively provide a unique, genome-wide picture of the epigenetic compartmentalization of the human genome and suggest that cell-lineage specification involves extensive reprogramming of replication timing patterns.