While classic machine learning paradigms assume training and test data are generated from the same process, domain adaptation addresses the more realistic setting in which the learner has large quantities of labeled data from some source task but limited or no labeled data from the target task it is attempting to learn. In this work, we give the first formal analysis showing that using active learning for domain adaptation yields a way to address the statistical challenges inherent in this setting. We propose a novel nonparametric algorithm, ANDA, that combines an active nearest neighbor querying strategy with nearest neighbor prediction. We provide analyses of its querying behavior and of finite sample convergence rates of the resulting classifier under covariate shift. Our experiments show that ANDA successfully corrects for dataset bias in multi-class image categorization.