We propose a mechanism linking legislative gridlock to voters’ support for candidates who hold extreme policy positions. Moderate voters rationally discount extreme policy proposals from co-partisans on gridlocked policy issues because on these issues policy change is unlikely. We test our mechanism in a large-scale online experiment in which we randomly vary subjects’ perceptions of gridlock and measure subjects’ support for co-partisan candidates in candidate-choice tasks. We verify that greater perception of gridlock on a specific issue increases moderate subjects’ propensity to vote for extreme co-partisan candidates on the gridlocked issue. We show that our experimental evidence is consistent with our mechanism and that other mechanisms are less likely to underlie our main result. Our theory offers a causal connection from gridlock to elite polarization that may inform further empirical work and suggests a novel tradeoff between elite polarization and policy stability in constitutional design.