Chromosomal regions can adopt stable and heritable alternative states resulting in bistable gene expression without changes to the DNA sequence. Such epigenetic control is often associated with alternative covalent modifications of histones. The stability and heritability of the states are thought to involve positive feedback where modified nucleosomes recruit enzymes that similarly modify nearby nucleosomes. We developed a simplified stochastic model for dynamic nucleosome modification based on the silent mating-type region of the yeast Schizosaccharomyces pombe. We show that the mechanism can give strong bistability that is resistant both to high noise due to random gain or loss of nucleosome modifications and to random partitioning upon DNA replication. However, robust bistability required: (1) cooperativity, the activity of more than one modified nucleosome, in the modification reactions and (2) that nucleosomes occasionally stimulate modification beyond their neighbor nucleosomes, arguing against a simple continuous spreading of nucleosome modification.