Heterochromatin normally has prescribed chromosomal positions and must not encroach on adjacent regions. We demonstrate that the fission yeast protein Epe1 stabilises silent chromatin, preventing the oscillation of heterochromatin domains. Epe1 loss leads to two contrasting phenotypes: alleviation of silencing within heterochromatin and expansion of silent chromatin into neighbouring euchromatin. Thus, we propose that Epe1 regulates heterochromatin assembly and disassembly, thereby affecting heterochromatin integrity, centromere function and chromosome segregation fidelity. Epe1 regulates the extent of heterochromatin domains at the level of chromatin, not via the RNAi pathway. Analysis of an ectopically silenced site suggests that heterochromatin oscillation occurs in the absence of heterochromatin boundaries. Epe1 requires predicted iron- and 2-oxyglutarate (2-OG)-binding residues for in vivo function, indicating that it is probably a 2-OG/Fe(II)-dependent dioxygenase. We suggest that, rather than being a histone demethylase, Epe1 may be a protein hydroxylase that affects the stability of a heterochromatin protein, or protein–protein interaction, to regulate the extent of heterochromatin domains. Thus, Epe1 ensures that heterochromatin is restricted to the domains to which it is targeted by RNAi.