In eukaryotes, the integrity of chromatin structure and organization is crucial to diverse key cellular processes from development to disease avoidance. To maintain the cell identity through mitotic cell generations, the genome (the genomic DNA sequence) as well as the epigenome (pertaining various forms of epigenetic information carriers, such as histone modifications, nucleosome positioning and the chromatin organization) is inherited with high fidelity. In comparison to the wealth of knowledge on genetic stability, we know much less on what may control the accuracy of epigenetic inheritance. In our recent work in the fission yeast Schizosaccharomyces pombe, by quantifying the epigenetic fidelity of CENP-A/Cnp1 or H3K9me2 nucleosome inheritance through cell divisions, we demonstrated that Ccp1, a homolog of histone chaperone Vps75 in budding yeast, participates in the modulation of centromeric nucleosomal epigenetic stability as well as proper heterochromatin organization. In this essay, we focus on discussing the uniquely high dynamicity of the subtelomeric heterochromatin regions and the complex mechanisms regulating epigenetic stability of centromeric chromatin.