RNA-protein interaction networks govern many biological processes but are difficult to examine comprehensively. We devised ribonucleoprotein networks analyzed by mutational profiling (RNP-MaP), a live-cell chemical probing strategy that maps cooperative interactions among multiple proteins bound to single RNA molecules at nucleotide resolution. RNP-MaP uses a hetero-bifunctional crosslinker to freeze interacting proteins in place on RNA and then maps multiple bound proteins on single RNA strands by read-through reverse transcription and DNA sequencing. RNP-MaP revealed that RNase P and RMRP, two sequence-divergent but structurally related non-coding RNAs, share RNP networks and that network hubs define functional sites in these RNAs. RNP-MaP also identified protein interaction networks conserved between mouse and human XIST long non-coding RNAs and defined protein communities whose binding sites colocalize and form networks in functional regions of XIST. RNP-MaP enables discovery and efficient validation of functional protein interaction networks on long RNAs in living cells.