Non-coding RNAs (ncRNAs) are transcribed throughout the genome and provide regulatory inputs to gene expression through their interaction with chromatin. The genomic targets and regulatory mechanisms of most ncRNAs remain unknown. Using chromatin-associated RNA sequencing (ChAR-seq) we obtained a global map of RNA-chromatin interactions, transcriptome and genome-wide, in human embryonic stem cells and definitive endoderm. We defined the overall architecture of the RNA-chromatin interactome that encompasses all long non-coding RNAs, intronic RNAs, as well as unannotated RNAs derived from regulatory elements, transposable elements, and intergenic regions. We show that the interactome is cell state specific, involves functionally diverse classes of RNAs, and can be accurately predicted by a simple model accounting for RNA expression and distance to their DNA targets. We show that nearly all ncRNAs exclusively interact with genes in close three-dimensional proximity to their transcription locus. We identified a small number of RNAs that deviate from that behavior and interact with many loci across the genome. By relating the changes in the interactome during differentiation to changes in gene expression, we demonstrate that activation or repression of individual genes is unlikely to be controlled by the activity of a single ncRNA.