Heterochromatin that depends on histone H3 lysine 9 methylation (H3K9me) renders embedded genes transcriptionally silent. In the fission yeast Schizosaccharomyces pombe, H3K9me heterochromatin can be transmitted through cell division provided the counteracting demethylase Epe1 is absent. Heterochromatin heritability might allow wild-type cells under certain conditions to acquire epimutations, which could influence phenotype through unstable gene silencing rather than DNA change. Here we show that heterochromatin-dependent epimutants resistant to caffeine arise in fission yeast grown with threshold levels of caffeine. Isolates with unstable resistance have distinct heterochromatin islands with reduced expression of embedded genes, including some whose mutation confers caffeine resistance. Forced heterochromatin formation at implicated loci confirms that resistance results from heterochromatin-mediated silencing. Our analyses reveal that epigenetic processes promote phenotypic plasticity, letting wild-type cells adapt to unfavourable environments without genetic alteration. In some isolates, subsequent or coincident gene-amplification events augment resistance. Caffeine affects two anti-silencing factors: Epe1 is downregulated, reducing its chromatin association, and a shortened isoform of Mst2 histone acetyltransferase is expressed. Thus, heterochromatin-dependent epimutation provides a bet-hedging strategy allowing cells to adapt transiently to insults while remaining genetically wild type. Isolates with unstable caffeine resistance show cross-resistance to antifungal agents, suggesting that related heterochromatin-dependent processes may contribute to resistance of plant and human fungal pathogens to such agents.