Abstract Debt matters for oil supply elasticities. We document the resiliency of oil production to the COVID-19-related collapse in demand due to indebtedness. We use exogenous variation in the timing of debt-related payments to identify financially constrained operators. We show that more financially constrained firms cut production by less than less-constrained firms and were less likely to complete new wells. To explore the mechanisms, we use borrowing-limit cuts and credit-line drawdowns to measure access to credit, and we exploit failed hedging practices. The propagation of oil demand shocks crucially depends on the indebtedness of the oil sector.