The promoter regions of active genes in the eukaryotic genome typically contain nucleosomes post-translationally modified with a trimethyl mark on histone H3 lysine 4 (H3K4), while transcriptional enhancers are marked with monomethylated H3K4. The flavin-dependent monoamine oxidase LSD1 (lysine-specific demethylase 1, also known as KDM1) demethylates mono- and dimethylated H3K4 in peptide substrates, but requires the corepressor protein, CoREST, to demethylate nucleosome substrates. The molecular basis for how the LSD1/CoREST complex interacts with its physiological nucleosome substrate remains largely unknown. We examine here the role of extranucleosomal DNA beyond the nucleosome core particle for LSD1/CoREST function. Our studies of LSD1/CoREST's enzyme activity and nucleosome binding show that extranucleosomal DNA dramatically enhances the activity of LSD1/CoREST, and that LSD1/CoREST binds to the nucleosome as a 1:1 complex. Our photocrosslinking experiments further indicate both LSD1 and CoREST subunits are in close contact with DNA around the nucleosome dyad as well as extranucleosomal DNA. Our results suggest that the LSD1/CoREST interacts with extranucleosomal DNA when it productively engages its nucleosome substrate.