Noncoding RNAs (ncRNAs) are an emerging class of regulatory molecules with a broad range of regulatory functions believed to be mediated by ncRNA-chromatin interactions. Genome-wide understanding of ncRNA functions requires precise mapping of all ncRNAs and their target loci. Current methods for studying chromatin-associated ncRNA lack specificity or are limited by throughput. We devised an unbiased strategy to identify all RNA Interactions with Chromatin by Paired-End-Taging (RICh-PET) and applied this approach to characterize the Drosophila RNA-chromatin interactome. We discovered that ncRNAs primarily target promoters and enhancers in open chromatin regions in colocalization with RNAPII and other TFs, suggesting combinatorial regulatory instructions for each locus. Enzymatic nuclear digestion followed by examination of specific chromatin loci indicated that ncRNAs collectively promote chromatin accessability, RNAPII-mediated interactions and overall 3D-genome organization. Our study demonstrates that RICh-PET and related methods represent a powerful suite of tools to interrogate the genome biology of ncRNAs.