RNA tertiary structure prediction has been based almost entirely on base-pairing constraints derived from phylogenetic covariation analysis. We describe here a complementary approach, inspired by the Rosetta low-resolution protein structure prediction method, that seeks the lowest energy tertiary structure for a given RNA sequence without using evolutionary information. In a benchmark test of 20 RNA sequences with known structure and lengths of approximately 30 nt, the new method reproduces better than 90% of Watson-Crick base pairs, comparable with the accuracy of secondary structure prediction methods. In more than half the cases, at least one of the top five models agrees with the native structure to better than 4 A rmsd over the backbone. Most importantly, the method recapitulates more than one-third of non-Watson-Crick base pairs seen in the native structures. Tandem stacks of "sheared" base pairs, base triplets, and pseudoknots are among the noncanonical features reproduced in the models. In the cases in which none of the top five models were native-like, higher energy conformations similar to the native structures are still sampled frequently but not assigned low energies. These results suggest that modest improvements in the energy function, together with the incorporation of information from phylogenetic covariance, may allow confident and accurate structure prediction for larger and more complex RNA chains.