Catalyzes the deacetylation of lysine residues on the N-terminal part of the core histones (H2A, H2B, H3 and H4). Histone deacetylation may constitute a tag for epigenetic repression and plays an important role in transcriptional regulation, cell cycle progression and developmental events. For instance, deacetylation of histone H3 may be a prerequisite for the subsequent recruitment of the histone methyltransferase Su(var)3-9 to histones. Involved in position-effect variegation (PEV).