In eukaryotic cells, genomic DNA replicates in a defined temporal order. The inactive X chromosome (Xi), the most extensive instance of facultative heterochromatin in mammals, replicates later than the active X chromosome (Xa), but the replication dynamics of inactive chromatin are not known. By profiling human DNA replication in an allele-specific, chromosomally phased manner, we determined for the first time the replication timing along the active and inactive chromosomes (Xa and Xi) separately. Replication of the Xi was different from that of the Xa, varied among individuals, and resembled a random, unstructured process. The Xi replicated rapidly and at a time largely separable from that of the euchromatic genome. Late-replicating, transcriptionally inactive regions on the autosomes also replicated in an unstructured manner, similar to the Xi. We conclude that DNA replication follows two strategies: slow, ordered replication associated with transcriptional activity, and rapid, random replication of silent chromatin. The two strategies coexist in the same cell, yet are segregated in space and time.