Anti-silencing function 1 (Asf1) and Chromatin Assembly Factor 1 (CAF-1) chaperone histones H3/H4 during the assembly of nucleosomes on newly replicated DNA. To understand the mechanism of histone H3/H4 transfer among Asf1, CAF-1 and DNA from a thermodynamic perspective, we developed and employed biophysical approaches using full-length proteins in the budding yeast system. We find that the C-terminal tail of Asf1 enhances the interaction of Asf1 with CAF-1. Surprisingly, although H3/H4 also enhances the interaction of Asf1 with the CAF-1 subunit Cac2, H3/H4 forms a tight complex with CAF-1 exclusive of Asf1, with an affinity weaker than Asf1-H3/H4 or H3/H4-DNA interactions. Unlike Asf1, monomeric CAF-1 binds to multiple H3/H4 dimers, which ultimately promotes the formation of (H3/H4)(2) tetramers on DNA. Thus, transition of H3/H4 from the Asf1-associated dimer to the DNA-associated tetramer is promoted by CAF-1-induced H3/H4 oligomerization.