Skepticism about the efficacy and efficiency of regulatory approaches has produced a wave of enthusiasm for market-based strategies for dealing with environmental conflicts. In the fisheries context, the most prominent of these strategies is the use of “catch shares,” which assign specific proportions of the total allowable catch to individuals who are then free to trade them with others. Catch shares are now in wide use domestically within many nations, and there are increasing calls for implementation of internationally tradable catch shares. Based on a review of theory, empirical evidence, and two contexts in which catch shares have been proposed, this Article explains why international catch shares are not likely to arrest the decline of ocean biodiversity. Catch shares were developed to promote greater economic efficiency and profitability in the fishing industry. They have proven capable of doing so at the domestic level, although their effects on wealth distribution have frequently been controversial. Theoretical and empirical support for the proposition that catch shares promote conservation, especially of non-target resources, is thinner. Furthermore, in the international context catch shares face special challenges. Catch shares cannot resolve the value differences that underlie the most intractable disagreements about international fisheries management. They are less likely to reduce conflicts over total allowable catch in the international than in the domestic context, because distrust of managers and competitors runs deeper. Finally, catch share strategies require effective enforcement, which is both institutionally and practically difficult to provide for many international fisheries. In general, catch shares are not a promising route to improving international fisheries management, and pursuing them could distract the international community from more important steps toward improving conservation of global ocean resources.