The HIRA histone chaperone complex is an epigenetic regulator responsible for deposition of histone variant H3.3-containing (H3.3/H4)2 tetramers into chromatin. Transcription-coupled histone deposition by the HIRA complex is essential during mammalian development and contributes to chromatin stability in both terminally differentiated and replicative cell types. Functional domains of the four complex subunits- HIRA, UBN1, CABIN1, and ASF1a- have been characterized and are largely conserved across eukaryotes, but little is understood about how these domains coordinate during transcription-coupled H3.3/H4 deposition. Here we utilize a full-length thermostable ortholog of CABIN1 to resolve a partial structure to 3.9Å by cryo-electron microscopy. We observe 1100 amino acid residues organized in helical repeats that provide a structural scaffold for complex assembly and function. We also observe a 6Å tunnel among the helical repeats containing unassigned density that is surrounded by basic and aromatic side chains. We hypothesize that this could serve as a single stranded RNA binding tunnel, demonstrate that the wild type protein binds single stranded RNA with a Kd of ~300 nM, and show that mutating two lysine residues in the tunnel weakens ssRNA binding. We also utilize truncated forms of human HIRA, UBN1, and ASF1a to characterize the stoichiometries and binding affinities of intermediate subcomplexes in the deposition process. Upon addition of ASF1a/H3.3/H4 to the HIRA/UBN1 scaffold, we show a stable heteropentameric complex with one copy each of HIRA, UBN1, ASF1a, H3.3, and H4. In the absence of ASF1a, a monomer-dimer equilibrium in which a monomer is defined as one copy each of HIRA, UBN1, H3.3, and H4 is observed. We conclude that HIRA/UBN1 multimerization is driven by histone tetramerization and proceed to show that histone binding to double stranded DNA likely ejects ASF1a and drives the deposition process. We apply our improved understanding of the HIRA chaperone complex to a revised functional model of transcription-coupled histone deposition in which histone tetramerization on DNA drives the deposition process while HIRA, UBN1, and CABIN1 provide a scaffold that positions histones while CABIN1 interacts with nascent single stranded RNA.