Little is known about the functional domain architecture of long noncoding RNAs (lncRNAs) because of a relative paucity of suitable methods to analyze RNA function at a domain level. Here we describe domain-specific chromatin isolation by RNA purification (dChIRP), a scalable technique to dissect pairwise RNA-RNA, RNA-protein and RNA-chromatin interactions at the level of individual RNA domains in living cells. dChIRP of roX1, a lncRNA essential for Drosophila melanogaster X-chromosome dosage compensation, reveals a 'three-fingered hand' ribonucleoprotein topology. Each RNA finger binds chromatin and the male-specific lethal (MSL) protein complex and can individually rescue male lethality in roX-null flies, thus defining a minimal RNA domain for chromosome-wide dosage compensation. dChIRP improves the RNA genomic localization signal by >20-fold relative to previous techniques, and these binding sites are correlated with chromosome conformation data, indicating that most roX-bound loci cluster in a nuclear territory. These results suggest dChIRP can reveal lncRNA architecture and function with high precision and sensitivity.