Hutchinson-Gilford progeria syndrome is a genetic disease caused by an aberrant form of Lamin A resulting in chromatin structure disruption, in particular by interfering with lamina associated domains. Early molecular alterations involved in chromatin remodeling have not been identified thus far. Here, we present SAMMY-seq, a high-throughput sequencing-based method for genome-wide characterization of heterochromatin dynamics. Using SAMMY-seq, we detect early stage alterations of heterochromatin structure in progeria primary fibroblasts. These structural changes do not disrupt the distribution of H3K9me3 in early passage cells, thus suggesting that chromatin rearrangements precede H3K9me3 alterations described at later passages. On the other hand, we observe an interplay between changes in chromatin accessibility and Polycomb regulation, with site-specific H3K27me3 variations and transcriptional dysregulation of bivalent genes. We conclude that the correct assembly of lamina associated domains is functionally connected to the Polycomb repression and rapidly lost in early molecular events of progeria pathogenesis.