Notch signaling plays a key role in many cell fate decisions during development by directing different gene expression programs via the transcription factor CSL, known as Su(H) in Drosophila Which target genes are responsive to Notch signaling is influenced by the chromatin state of enhancers, yet how this is regulated is not fully known. Detecting a specific increase in the histone variant H3.3 in response to Notch signaling, we tested which chromatin remodelers or histone chaperones are required for the changes in enhancer accessibility to Su(H) binding. We show a crucial role for the Brahma SWI/SNF chromatin remodeling complex, including the actin-related BAP55 subunit, in conferring enhancer accessibility and enabling the transcriptional response to Notch activity. The Notch-responsive regions have high levels of nucleosome turnover which depend on the Brahma complex, increase in magnitude with Notch signaling, and primarily involve histone H3.3. Together these results highlight the importance of SWI/SNF-mediated nucleosome turnover in rendering enhancers responsive to Notch.