The yeast SWR1 complex catalyzes the exchange of histone H2A/H2B dimers in nucleosomes with Htz1/H2B dimers. We use cryoelectron microscopy to determine the structure of an enzyme-bound hexasome intermediate in the reaction pathway of histone exchange, in which an H2A/H2B dimer has been extracted from a nucleosome prior to the insertion of a dimer comprising Htz1/H2B. The structure reveals a key role for the Swc5 subunit in stabilizing the unwrapping of DNA from the histone core of the hexasome. By engineering a crosslink between an Htz1/H2B dimer and its chaperone protein Chz1, we show that this blocks histone exchange by SWR1 but allows the incoming chaperone-dimer complex to insert into the hexasome. We use this reagent to trap an SWR1/hexasome complex with an incoming Htz1/H2B dimer that shows how the reaction progresses to the next step. Taken together the structures reveal insights into the mechanism of histone exchange by SWR1 complex.