This paper provides a general framework for analyzing the stability of stablecoins, cryptocurrencies pegged to a traditional currency. We study the problem of a monopolist platform that can earn seigniorage revenues from issuing stablecoins. We characterize stablecoin issuance-redemption and pegging dynamics under various degrees of commitment to policies. Even under full commitment, the stablecoin peg is vulnerable to large demand shocks. Backing stablecoins with collateral helps to stabilize the platform but is costly for the platform’s equity (token) holders. Combined with collateral, decentralization can act as a substitute for commitment.