We consider a model of elections in which two office-motivated candidates are uncertain about the location of the median voter's ideal point, and in which candidates receive private signals about the location of the median prior to taking policy positions. Assuming signal spaces are finite, we show that there is at most one pure strategy equilibrium and give a sharp characterization, if one exists: after receiving a signal, each candidate locates at the median of the distribution of the median voter, conditional on the other candidate receiving the same signal. A candidate's position, conditional on his/her signal, is therefore a biased estimate of the true median, with candidate positions tending to the extremes of the policy space. We give sufficient conditions for existence of pure strategy equilibria. We characterize mixed strategy equilibria in a special case of the model.