Epigenetic inheritance mechanisms play fundamental roles in maintaining cellular memory of gene expression states. In fission yeast, histone H3 lysine 9 (H3K9) is methylated (H3K9me) at heterochromatic domains. These domains can be epigenetically inherited when epe1+, encoding an enzyme that promotes H3K9 demethylation, is deleted. How native epigenetic states are stably maintained in epe1+ cells remains unknown. Here, we developed a system to examine the role of DNA sequence and genomic context in propagation of a cis-heritable H3K9me-dependent silenced state. We show that in epe1+ cells, in addition to sequence-independent mechanisms that propagate H3K9me, epigenetic inheritance of silencing requires binding sites for sequence-dependent activating transcription factor (ATF)–adenosine 3′,5′-monophosphate (cAMP) response element–binding protein (CREB) family transcription factors within their native chromosomal context. Thus, specific DNA sequences contribute to cis inheritance of H3K9me and silent epigenetic states.