After mitosis, mammalian chromosomes partially decondense to occupy distinct territories in the cell nucleus. Current models propose that territories are separated by an interchromatin domain, rich in soluble nuclear machinery, where only rare interchromosomal interactions can occur via extended chromatin loops. In contrast, recent evidence for chromatin mobility and high frequency of chromosome translocations are consistent with significant levels of chromosome intermingling, with important consequences for genome function and stability. Here we use a novel high-resolution in situ hybridization procedure that preserves chromatin nanostructure to show that chromosome territories intermingle significantly in the nucleus of human cells. The degree of intermingling between specific chromosome pairs in human lymphocytes correlates with the frequency of chromosome translocations in the same cell type, implying that double-strand breaks formed within areas of intermingling are more likely to participate in interchromosomal rearrangements. The presence of transcription factories in regions of intermingling and the effect of transcription impairment on the interactions between chromosomes shows that transcription-dependent interchromosomal associations shape chromosome organization in mammalian cells. These findings suggest that local chromatin conformation and gene transcription influence the extent with which chromosomes interact and affect their overall properties, with direct consequences for cell-type specific genome stability.