The HIRA histone chaperone complex is composed of the proteins HIRA, UBN1, and CABIN1 that cooperate with ASF1a to specifically mediate deposition of H3.3/H4 into chromatin. While many of the protein/protein contacts that allow for assembly of this multi-protein histone chaperone complex have been elucidated, how these proteins are able to cooperate to specifically bind and deposit H3.3/H4 over H3.1/H4, which differ by only 5 amino acids, has remained unclear. Here we demonstrate the HIRA complex subunit UBN1 specifically binds to H3.3/H4 over H3.1/H4 using a combination of biochemical and structural studies. We show H3.3-specific binding is mediated by highly conserved residues in the UBN1 Hpc2-related domain (HRD) and residue G90 in H3.3. Interestingly the UBN1 HRD and another H3.3-specific histone chaperone, Daxx, bind to H3.3/H4 in the region of G90 with striking similarity. Using sequence conservation and secondary structure prediction we have identified the UBN1 middle domain. We show the middle domain is able to form monomer and dimer populations as well as bind to H3/H4 through interaction with the N-terminal histone tails. We have additionally discovered that a loop region linking the UBN1 HRD and middle domains binds non-specifically to DNA with nanomolar affinity, although UBN1 fragments containing the HRD, DNA binding loop, and middle domain are unable to bind assembled nucleosomes. Finally we demonstrate with analytical ultracentrifugation that the HIRA C-terminal domain forms a stable trimer and interacts with CABIN1 in a HIRA(3)/CABIN1(2) stoichiometry. We show that the HIRA C-terminal domain is organized into separate strand and helical regions that must be linked for trimer formation. Further we show that a replisome protein called Ctf4 is structurally related to HIRA, as it also arranges into a trimer composed of separate strand and helical regions and interacts in a 3:2 stoichiometry with binding partners. From these observations we propose a model for H3.3/H4 deposition by the HIRA complex involving DNA binding and dimer formation by UBN1 to mediate (H3.3/H4)2 tetramer formation organized on a HIRA(3)/UBN1(3)/CABIN1(2) complex where the third UBN1 molecule may harbor ASF1a/H3.3/H4 in reserve.