Defective DNA repair causes Fanconi anemia (FA), a rare childhood cancer–predisposing syndrome. At least 15 genes are known to be mutated in FA; however, their role in DNA repair remains unclear. Here, we show that the FANCJ helicase promotes DNA replication in trans by counteracting fork stalling on replication barriers, such as G4 quadruplex structures. Accordingly, stabilization of G4 quadruplexes in ΔFANCJ cells restricts fork movements, uncouples leading- and lagging-strand synthesis and generates small single-stranded DNA gaps behind the fork. Unexpectedly, we also discovered that FANCJ suppresses heterochromatin spreading by coupling fork movement through replication barriers with maintenance of chromatin structure. We propose that FANCJ plays an essential role in counteracting chromatin compaction associated with unscheduled replication fork stalling and restart, and suppresses tumorigenesis, at least partially, in this replication-specific manner.