Modular domains of long non-coding RNAs can serve as scaffolds to bring distant regions of the linear genome into spatial proximity. Here, we present HiChIRP, a method leveraging bio-orthogonal chemistry and optimized chromosome conformation capture conditions, which enables interrogation of chromatin architecture focused around a specific RNA of interest down to approximately ten copies per cell. HiChIRP of three nuclear RNAs reveals insights into promoter interactions (7SK), telomere biology (telomerase RNA component) and inflammatory gene regulation (lincRNA-EPS).