Chromatin interactions and linkage disequilibrium (LD) are both pairwise measurements between genomic loci that show block patterns along mammalian chromosomes. Their values are generally high for sites that are nearby in the linear genome but abruptly drop across block boundaries. One function of chromatin boundaries is to insulate regulatory domains from one another. Since recombination is depressed within genes and between distal regulatory elements and their promoters, we hypothesized that LD and chromatin contact frequency might be correlated genome-wide with the boundaries of LD blocks and chromatin domains frequently coinciding. To comprehensively address this question, we compared chromatin contacts in 22 cell types to LD across billions of pairs of loci in the human genome. These computationally intensive analyses revealed that there is no concordance between LD and chromatin interactions, even at genomic distances below 25 kilobases (kb) where both tend to be high. At genomic distances where LD is approximately zero, chromatin interactions are frequent. While LD is somewhat elevated between distal regulatory elements and their promoters, LD block boundaries are depleted-not enriched-at chromatin boundaries. Finally, gene expression and ontology data suggest that chromatin contacts identify regulatory variants more reliably than do LD and genomic proximity. We conclude that the genomic architectures of genetic and physical interactions are independent, with important implications for gene regulatory evolution, interpretation of genetic association studies, and precision medicine.