A fraction of a genetically homogeneous microbial population may survive exposure to stress such as antibiotic treatment. Unlike resistant mutants, cells regrown from such persistent bacteria remain sensitive to the antibiotic. We investigated the persistence of single cells of Escherichia coli with the use of microfluidic devices. Persistence was linked to preexisting heterogeneity in bacterial populations because phenotypic switching occurred between normally growing cells and persister cells having reduced growth rates. Quantitative measurements led to a simple mathematical description of the persistence switch. Inherent heterogeneity of bacterial populations may be important in adaptation to fluctuating environments and in the persistence of bacterial infections.