Approximately 75% of the human genome is transcribed, the majority of which does not encode protein. However, many noncoding RNAs (ncRNAs) are rapidly degraded after transcription, and relatively few have established functions, questioning the significance of this observation. Here we show that esBAF, a SWI/SNF family nucleosome remodeling factor, suppresses transcription of ncRNAs from approximately 57,000 nucleosome-depleted regions (NDRs) throughout the genome of mouse embryonic stem cells (ESCs). We show that esBAF functions to both keep NDRs nucleosome-free and promote elevated nucleosome occupancy adjacent to NDRs. Reduction of adjacent nucleosome occupancy upon esBAF depletion is strongly correlated with ncRNA expression, suggesting that flanking nucleosomes form a barrier to pervasive transcription. Upon forcing nucleosome occupancy near two NDRs using a nucleosome-positioning sequence, we found that esBAF is no longer required to silence transcription. Therefore, esBAF's function to enforce nucleosome occupancy adjacent to NDRs, and not its function to maintain NDRs in a nucleosome-free state, is necessary for silencing transcription over ncDNA. Finally, we show that the ability of a strongly positioned nucleosome to repress ncRNA depends on its translational positioning. These data reveal a novel role for esBAF in suppressing pervasive transcription from open chromatin regions in ESCs.