Modular domains of lncRNAs can serve as scaffolds to bring distant regions of the linear genome into spatial proximity. Here we present HiChIRP, a method leveraging novel bioorthogonal chemistry and customized 3C conditions, that enables interrogation of chromatin architecture focused around a specific RNA of interest down to ~10 copies per cell. HiChIRP of three nuclear RNAs reveal insights into promoter interactions (7SK), telomere biology (TERC), and inflammatory gene regulation (lincRNA-EPS).