The nuclear lamina (NL) interacts with hundreds of large genomic regions termed lamina associated domains (LADs). The dynamics of these interactions and the relation to epigenetic modifications are poorly understood. We visualized the fate of LADs in single cells using a "molecular contact memory" approach. In each nucleus, only ~30% of LADs are positioned at the periphery; these LADs are in intermittent molecular contact with the NL but remain constrained to the periphery. Upon mitosis, LAD positioning is not detectably inherited but instead is stochastically reshuffled. Contact of individual LADs with the NL is linked to transcriptional repression and H3K9 dimethylation in single cells. Furthermore, we identify the H3K9 methyltransferase G9a as a regulator of NL contacts. Collectively, these results highlight principles of the dynamic spatial architecture of chromosomes in relation to gene regulation.