This paper contributes to existing climate finance literature by examining how firms' proactive management of carbon risks affects market assessment of their credit risk. Using two quasi-exogenous events involving the 2015 Paris Climate Agreement and the staggered implementation of U.S. state climate adaptation plans, we find that stronger carbon risk management is associated with significantly lower credit default swap spreads. Our results are not driven by firm-level climate exposure, and social or governance risk. Firms with better carbon risk management also exhibit lower subsequent carbon emissions. Our paper highlights the importance of carbon risk management in mitigating credit risk.