Misinformation pervades political competition. We introduce opportunities for political candidates and their media supporters to spread fake news about the policy environment and perhaps about parties' positions into a familiar model of electoral competition. In the baseline model with full information, the parties' positions converge to those that maximize aggregate welfare. When parties can broadcast fake news to audiences that disproportionately include their partisans, policy divergence and suboptimal outcomes can result. We study a sequence of models that impose progressively tighter constraints on false reporting and characterize situations that lead to divergence and a polarized electorate.