A small fraction of cells in many bacterial populations, called persisters, are much less sensitive to antibiotic treatment than the majority. Persisters are in a dormant metabolic state, even while remaining genetically identical to the actively growing cells. Toxin and antitoxin modules in bacteria are believed to be one possible cause of persistence. A two-gene operon, HipBA, is one of many chromosomally encoded toxin and antitoxin modules in Escherichia coli and the HipA7 allelic variant was the first validated high-persistence mutant. Here, we present a stochastic model that can generate bistability of the HipBA system, via the reciprocal coupling of free HipA to the cellular growth rate. The actively growing state and the dormant state each correspond to a stable state of this model. Fluctuations enable transitions from one to the other. This model is fully in agreement with experimental data obtained with synthetic promoter constructs.