The histone chaperone FACT occupies transcribed regions where it plays prominent roles in maintaining chromatin integrity and preserving epigenetic information. How it is targeted to transcribed regions, however, remains unclear. Proposed models include docking on the RNA polymerase II (RNAPII) C-terminal domain (CTD), recruitment by elongation factors, recognition of modified histone tails, and binding partially disassembled nucleosomes. Here, we systematically test these and other scenarios in Saccharomyces cerevisiae and find that FACT binds transcribed chromatin, not RNAPII. Through a combination of high-resolution genome-wide mapping, single-molecule tracking, and mathematical modeling, we propose that FACT recognizes the +1 nucleosome, as it is partially unwrapped by the engaging RNAPII, and spreads to downstream nucleosomes aided by the chromatin remodeler Chd1. Our work clarifies how FACT interacts with genes, suggests a processive mechanism for FACT function, and provides a framework to further dissect the molecular mechanisms of transcription-coupled histone chaperoning. Display omitted •High-resolution mapping and single-molecule tracking of FACT in yeast•FACT binds partially unwrapped nucleosomes in transcribed genes, not RNAPII•FACT distribution along genes requires Chd1•Processive mechanism for FACT function Preserving nucleosomes during transcription elongation requires histone chaperone FACT and chromatin remodeler Chd1, but their interplay is unclear. Here, Jeronimo et al. show that nucleosomal DNA unraveling by RNAPII drives the recruitment of FACT, while the remodeling activity of Chd1 promotes FACT movement along genes, enabling a processive mechanism.