An extensive literature identifies how rational people who observe the behavior of other privately-informed rational people with similar tastes may come to imitate them. While most of the literature explores when and how such imitation leads to inefficient information aggregation, this paper instead explores the behavior of fully rational observational learners. In virtually any setting, they imitate only some of their predecessors, and sometimes contradict both their private information and the prevailing beliefs that they observe. In settings that allow players to extract all relevant information about others' private signals from their actions, we identify necessary and sufficient conditions for rational observational learning to include "anti-imitation" where, fixing other observed actions, a person regards a state of the world as less likely the more a predecessor's action indicates belief in that state. Anti-imitation arises from players' need to subtract off the sources of correlation in others' actions, and is mandated by rationality in settings where players observe many predecessors' actions but not all recent or concurrent ones. Moreover, in these settings, there is always a positive probability that some player plays contrary to both her private information and the beliefs of every single person whose action she observes. We illustrate a setting where a society of fully rational players nearly always converges to the truth via an arbitrarily large number of such episodes of extreme contrarian behavior.