Since the global financial crisis, interest rate swap rates, which represent future uncollateralized interbank borrowing, have fallen below maturity-matched Treasury rates. This is surprising, because US Treasuries, which are deemed expensive because of superior liquidity and safety, should produce yields that are lower than those of swap rates. We show, by no-arbitrage, that sovereign default risk explains negative swap spreads even without frictions such as balance sheet constraints, convenience yield, and hedging demand. We support this explanation with an equilibrium model that jointly accounts for macroeconomic fundamentals and the term structures of interest and US credit default swap rates.