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Higher-order chromatin structure arises from the combinatorial physical interactions of many genomic loci. To investigate this aspect of genome architecture we developed Pore-C, which couples chromatin conformation capture with Oxford Nanopore Technologies (ONT) long reads to directly sequence multi-way chromatin contacts without amplification. In GM12878, we demonstrate that the pairwise interaction patterns implicit in Pore-C multi-way contacts are consistent with gold standard Hi-C pairwise contact maps at the compartment, TAD, and loop scales. In addition, Pore-C also detects higher-order chromatin structure at 18.5-fold higher efficiency and greater fidelity than SPRITE, a previously published higher-order chromatin profiling technology. We demonstrate Pore-C's ability to detect and visualize multi-locus hubs associated with histone locus bodies and active / inactive nuclear compartments in GM12878. In the breast cancer cell line HCC1954, Pore-C contacts enable the reconstruction of complex and aneuploid rearranged alleles spanning multiple megabases and chromosomes. Finally, we apply Pore-C to generate a chromosome scale de novo assembly of the HG002 genome. Our results establish Pore-C as the most simple and scalable assay for the genome-wide assessment of combinatorial chromatin interactions, with additional applications for cancer rearrangement reconstruction and de novo genome assembly. Chromatin structure | Structural variation | Long read sequencing | De novo genome assembly | cancer genomicsCorrespondence: mski@mskilab.org