Global Systemically Important Banks (GSIBs) face additional capital requirements and closer supervision. We study how closer supervision affects corporate credit supply and investigate consequences for firms. GSIB designations reduce lending on average by 5.9% but to risky firms by 7.2%. The consequences are lower asset, sales, and investment growth, especially among high-risk borrowers, and reduced R&D expenditures among all GSIB-dependent firms. Closer supervision therefore reduces banks' risk-taking but has potentially unintended implications for firms' ability to finance innovation, which seems to crucially depend on bank credit. The supervision-induced effects are larger than those attributed to GSIB-specific capital surcharges.