Putting a price on carbon emissions helps mitigate climate change but may also raise overall price inflation. Using high-frequency event studies based on regulatory news in the European carbon market, we show that carbon price surprises generate significant increases not only in energy futures prices, but also in inflation swap prices and breakeven inflation rates. These measures of market-based inflation expectations respond positively at both short and long horizons, with significant effects up to ten years out. Such long-lived inflationary consequences of climate policy are relevant for central banks. However, despite the sustained increases in market-based inflation expectations, forward-looking nominal interest rates show no meaningful response to the carbon policy shocks, suggesting that investors do not anticipate that the European Central Bank will lean against the inflationary effects of higher carbon prices.