Many experts believe that AI systems will sooner or later pose uninsurable risks, including existential risks. This creates an extreme judgment-proof problem: few if any parties can be held accountable ex post in the event of such a catastrophe. This paper proposes a novel solution: a government-provided, mandatory indemnification program for AI developers. The program uses risk-priced indemnity fees to induce socially optimal levels of care. Risk-estimates are determined by surveying experts, including indemnified developers. The Bayesian Truth Serum mechanism is employed to incent honest and effortful responses. Compared to alternatives, this approach arguably better leverages all private information, and provides a clearer signal to indemnified developers regarding what risks they must mitigate to lower their fees. It's recommended that collected fees be used to help fund the safety research developers need, employing a fund matching mechanism (Quadratic Financing) to induce an optimal supply of this public good. Under Quadratic Financing, safety research projects would compete for private contributions from developers, signaling how much each is to be supplemented with public funds.