Randomization is an essential component of clinical trials because it balances covariates between the treatment groups. However, randomization only balances covariates in expectation, and in any one particular allocation, covariates may be unbalanced simply by chance. This covariate imbalance is not a rare unlucky occurrence, but actually a quite likely possibility in clinical trials with a large number of covariates. In the case of substantial covariate imbalance, rather than proceeding with a comprised clinical trial, we propose rerandomizing. Rerandomization involves, first, explicitly specifying a specific criterion for acceptable covariate balance before initiating randomization; then randomizing units into treatment groups and checking balance before conducting the experiment; and rerandomizing until the specified criterion is met. If results are analyzed with a randomization test that takes the rerandomization procedure into account, valid frequentist properties, such as accurate p-values and Type 1 error rates, are maintained. When the covariates being balanced are correlated with the outcome, rerandomization also increases the power of tests. Rerandomization is flexible, and can adapt to a variety of different clinical trial settings.