A standard assumption in supervised learning is that the training data and test data are from the same distribution. However, this assumption often fails to hold in practice, which can cause the learned model to perform poorly. We consider the problem of detecting covariate shift, where the covariate distribution shifts but the conditional distribution of labels given covariates remains the same. This problem can naturally be solved using a two-sample test—i.e., test whether the current test distribution of covariates equals the training distribution of covariates. Our algorithm builds on classifier tests, which train a discriminator to distinguish train and test covariates, and then use the accuracy of this discriminator as a test statistic. A key challenge is that classifier tests assume given a fixed set of test covariates. In practice, test covariates often arrive sequentially over time—e.g., a self-driving car observes a stream of images while driving. Furthermore, covariate shift can occur multiple times—i.e., shift and then shift back later or gradually shift over time. To address these challenges, our algorithm trains the discriminator online. Additionally, it evaluates test accuracy using each new covariate before taking a gradient step; this strategy avoids constructing a held-out test set, which can improve sample efficiency. We prove that this optimization preserves the correctness—i.e., our algorithm achieves a desired bound on the false positive rate. In our experiments, we show that our algorithm efficiently detects covariate shifts on multiple datasets—ImageNet, IWildCam, and Py150.