Hutchinson-Gilford progeria syndrome (HGPS) is a premature aging disease that is frequently caused by a de novo point mutation at position 1824 in LMNA. This mutation activates a cryptic splice donor site in exon 11, and leads to an in-frame deletion within the prelamin A mRNA and the production of a dominant negative lamin A protein, known as progerin. Here we show that HGPS cells experience genome-wide alterations in patterns of H3K27me3 deposition, changes in the associations of genomic loci with nuclear lamin A/C, and, at late passages, genome-wide loss of spatial compartmentalization of active and inactive chromatin domains that characterizes chromosome folding in normal cells. We further demonstrate that the H3K27me3 changes associate with gene expression alterations in HGPS cells. Our results support a model that the accumulation of progerin in the nuclear lamina leads to altered H3K27me3 marks in heterochromatin, possibly through the down-regulation of EZH2, and disrupts heterochromatin-lamina interactions. These changes may then lead to the genomic disorganization and changes in transcriptional regulation we observe in HGPS fibroblasts.