The biological behaviors of ribozymes, riboswitches, and numerous other functional RNA molecules are critically dependent on their tertiary folding and their ability to sample multiple functional states. The conformational heterogeneity and partially folded nature of most of these states has rendered their characterization by high-resolution structural approaches difficult or even intractable. Here we introduce a method to rapidly infer the tertiary helical arrangements of large RNA molecules in their native and non-native solution states. Multiplexed hydroxyl radical (.OH) cleavage analysis (MOHCA) enables the high-throughput detection of numerous pairs of contacting residues via random incorporation of radical cleavage agents followed by two-dimensional gel electrophoresis. We validated this technology by recapitulating the unfolded and native states of a well studied model RNA, the P4-P6 domain of the Tetrahymena ribozyme, at subhelical resolution. We then applied MOHCA to a recently discovered third state of the P4-P6 RNA that is stabilized by high concentrations of monovalent salt and whose partial order precludes conventional techniques for structure determination. The three-dimensional portrait of a compact, non-native RNA state reveals a well ordered subset of native tertiary contacts, in contrast to the dynamic but otherwise similar molten globule states of proteins. With its applicability to nearly any solution state, we expect MOHCA to be a powerful tool for illuminating the many functional structures of large RNA molecules and RNA/protein complexes.