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Genome-wide association studies have identified more than 70 common variants that are associated with breast cancer risk. Most of these variants map to non-protein-coding regions and several map to gene deserts, regions of several hundred kilobases lacking protein-coding genes. We hypothesized that gene deserts harbor long-range regulatory elements that can physically interact with target genes to influence their expression. To test this, we developed Capture Hi-C (CHi-C), which, by incorporating a sequence capture step into a Hi-C protocol, allows high-resolution analysis of targeted regions of the genome. We used CHi-C to investigate long-range interactions at three breast cancer gene deserts mapping to 2q35, 8q24.21, and 9q31.2. We identified interaction peaks between putative regulatory elements ("bait fragments") within the captured regions and "targets" that included both protein-coding genes and long noncoding (Inc) RNAs over distances of 6.6 kb to 2.6 Mb. Target protein-coding genes were IGFBP5, KLF4, NSMCE2, and MYC; and target IncRNAs included DIRC3, PVT1, and CCDC26. For one gene desert, we were able to define two SNPs (rs12613955 and rs4442975) that were highly correlated with the published risk variant and that mapped within the bait end of an interaction peak. In vivo ChIP-qPCR data show that one of these, rs4442975, affects the binding of FOXA1 and implicate this SNP as a putative functional variant.