The mechanisms by which histones are disassembled and reassembled into nucleosomes and chromatin structure during DNA replication, repair and transcription are poorly understood. A better understanding of the processes involved is, however, crucial if we are to understand whether and how histone variants and post-translationally modified histones are inherited in an epigenetic manner. To this end we have studied the interaction of the histone H3-H4 complex with the human retinoblastoma-associated protein RbAp48 and their exchange with a second histone chaperone, anti-silencing function protein 1 (ASF1). Exchange of histones H3-H4 between these two histone chaperones has a central role in the assembly of new nucleosomes, and we show here that the H3-H4 complex has an unexpected structural plasticity, which is important for this exchange.