Long non-coding RNAs (lncRNAs) constitute a significant fraction of the transcriptome, playing important roles in development and disease. However, our understanding of structure-function relationships for this emerging class of RNAs has been limited to secondary structures. Here, we report the 3-D atomistic structural study of epigenetic lncRNA, Braveheart (Bvht), and its complex with CNBP (Cellular Nucleic acid Binding Protein). Using small angle X-ray scattering (SAXS), we elucidate the ensemble of Bvht RNA conformations in solution, revealing that Bvht lncRNA has a well-defined, albeit flexible 3-D structure that is remodeled upon CNBP binding. Our study suggests that CNBP binding requires multiple domains of Bvht and the RHT/AGIL RNA motif. We show that RHT/AGIL, previously shown to interact with CNBP, contains a highly flexible loop surrounded by more ordered helices. As one of the largest RNA-only 3-D studies, the work lays the foundation for future structural studies of lncRNA-protein complexes.