Epigenetics is the study of heritable changes in gene expression without concomitant changes in DNA sequence. Due to its relevance in development, differentiation and human health, epigenetics has recently become an emerging area of science with regard to eukaryotic organisms and has shown enormous potential in synthetic biology. However, significant examples of epigenetic regulation in bacterial synthetic biology have not yet been reported. In the current study, we present the first model of such an epigenetic circuit. We termed the circuit the alternator circuit because parental cells carrying this circuit and their progeny alternate between distinct and heritable cellular fates without undergoing changes in genome sequence. Furthermore, we demonstrated that the alternator circuit exhibits hysteresis because its output depends not only on its present state but also on its previous states.