This paper proposes a new market-based approach to the bankruptcy problem. A hypothetical claims market, where creditors can trade their claims prior to the allocation of the liquidation value, is considered. The introduction of the claims market opens an atypical arbitrage opportunity, which allows creditors to make profits even by buying and selling the same amount of claims at the same price. This anomaly occurs because the claims market enables the creditors to exploit any sensitivity of a bankruptcy rule to a change in the distribution of claims, and is ruled out by requiring that the bankruptcy rule satisfy a no-arbitrage condition. The no-arbitrage condition turns out to be a necessary and sufficient condition for the existence of equilibrium in the claims market. All equilibria are shown to be equivalent to the outcome of the proportional rule. A connection between the market-based approach and the axiomatic approach is developed and simpler characterizations of the proportional rule are derived. A new normative foundation for the proportional rule is also established.