The 30-year U.S. swap spreads have been negative since September 2008. We offer a novel explanation for this persistent anomaly. Through an illustrative model, we show that underfunded pension plans optimally use swaps for duration hedging. Combined with dealer banks' balance sheet constraints, this demand can drive swap spreads to become negative. Empirically, we construct a measure of the aggregate funding status of defined benefit pension plans and show that this measure helps explain 30-year swap spreads. We find a similar link between pension funds' underfunding and swap spreads for two other regions.