In a monetary union, the risk-free rate cannot adjust to country-level fiscal positions, leaving only default spreads and convenience yields to respond. Empirically, we find that convenience yields explain a large share of the variation in eurozone (EZ) sovereign bond yields. EZ sovereign bonds earn larger convenience yields when their governments run larger surpluses. Since convenience yields generate substantial seigniorage revenue from debt issuance, our estimates imply economically large fiscal costs from low convenience yields for peripheral countries in the EZ.