The organization of DNA within the eukaryotic nucleus is important for cellular processes such as regulation of gene expression and repair of DNA damage. To comprehend cell-to-cell variation within a complex system, systematic analysis of individual cells is necessary. While many tools exist to capture DNA conformation and chromatin context, these methods generally require large populations of cells for sufficient output. Here we describe single-cell DamID, a technique to capture contacts between DNA and a given protein of interest. By fusing the bacterial methyltransferase Dam to nuclear lamina protein lamin B1, genomic regions in contact with the nuclear periphery can be mapped. Single-cell DamID generates contact maps with sufficient throughput and resolution to reliably identify patterns of similarity as well as variation in nuclear organization of interphase chromosomes.