Controlled experimental evolution during antibiotic treatment can help to explain the processes leading to antibiotic resistance in bacteria. Recently, intermittent antibiotic exposures have been shown to lead rapidly to the evolution of tolerance—that is, the ability to survive under treatment without developing resistance. However, whether tolerance delays or promotes the eventual emergence of resistance is unclear. Here we used in vitro evolution experiments to explore this question. We found that in all cases, tolerance preceded resistance. A mathematical population-genetics model showed how tolerance boosts the chances for resistance mutations to spread in the population. Thus, tolerance mutations pave the way for the rapid subsequent evolution of resistance. Preventing the evolution of tolerance may offer a new strategy for delaying the emergence of resistance.