We describe tethered conformation capture (TCC), a method for genome-wide mapping of chromatin interactions. By performing ligations on solid substrates rather than in solution, TCC substantially enhances the signal-to-noise ratio, thereby facilitating a detailed analysis of interactions within and between chromosomes. We identified a group of regions in each chromosome in human cells that account for the majority of interchromosomal interactions. These regions are marked by high transcriptional activity, suggesting that their interactions are mediated by transcriptional machinery. Each of these regions interacts with numerous other such regions throughout the genome in an indiscriminate fashion, partly driven by the accessibility of the partners. As a different combination of interactions is likely present in different cells, we developed a computational method to translate the TCC data into physical chromatin contacts in a population of three-dimensional genome structures. Statistical analysis of the resulting population demonstrates that the indiscriminate properties of interchromosomal interactions are consistent with the well-known architectural features of the human genome.