The accessibility of DNA to regulatory proteins is a major property of the chromatin environment that favours or hinders transcription. Recent studies in flies reported that H3K9me2-marked heterochromatin is accessible while H3K27me3-marked chromatin forms extensive domains of low accessibility. Here we show that plants regulate DNA accessibility differently. H3K9me2-marked heterochromatin is the least accessible in the Arabidopsis thaliana genome, and H3K27me3-marked chromatin also has low accessibility. We see that very long genes without H3K9me2 or H3K27me3 are often inaccessible and generated significantly lower amounts of antisense transcripts than other genes, suggesting that reduced accessibility is associated with reduced recognition of alternative promoters. Low accessibility of H3K9me2-marked heterochromatin and long genes depend on cytosine methylation, explaining why chromatin accessibility differs between plants and flies. Together, we conclude that restriction of DNA accessibility is a local property of chromatin and not necessarily a consequence of microscopically visible compaction.