The sea lamprey (Petromyzon marinus) represents one of the few vertebrate species known to undergo large-scale programmatic elimination of genomic DNA over the course of its normal development. Programmed genome rearrangements (PGRs) result in the reproducible loss of ~20% of the genome from somatic cell lineages during early embryogenesis. Studies of PGR hold the potential to provide novel insights related to the maintenance of genome stability during the cell cycle and coordination between mechanisms responsible for the accurate distribution of chromosomes into daughter cells, yet little is known regarding the mechanistic basis or cellular context of PGR in this or any other vertebrate lineage. Here we identify epigenetic silencing events that are associated with the programmed elimination of DNA and describe the spatiotemporal dynamics of PGR during lamprey embryogenesis. In situ analyses reveal that the earliest DNA methylation (and to some extent H3K9 trimethylation) events are limited to specific extranuclear structures (micronuclei) containing eliminated DNA. During early embryogenesis a majority of micronuclei (~60%) show strong enrichment for repressive chromatin modifications (H3K9me3 and 5meC). These analyses also led to the discovery that eliminated DNA is packaged into chromatin that does not migrate with somatically retained chromosomes during anaphase, a condition that is superficially similar to lagging chromosomes observed in some cancer subtypes. Closer examination of "lagging" chromatin revealed distributions of repetitive elements, cytoskeletal contacts and chromatin contacts that provide new insights into the cellular mechanisms underlying the programmed loss of these segments. Our analyses provide additional perspective on the cellular and molecular context of PGR, identify new structures associated with elimination of DNA and reveal that PGR is completed over the course of several successive cell divisions.