This paper provides a general model of stablecoins, cryptocurrencies pegged to a traditional currency. We characterize the optimal design of a stablecoin protocol that generates seigniorage fees from issuance. We use this framework to assess the ability of various protocol designs to maintain the peg. Our model rationalizes algorithmic backing of stablecoins but highlights its greater fragility relative to collateralization. Immutable smart contracts improve stability because the issuer suffers from a commitment problem. Even under full collateralization, promises to repurchase stablecoins when demand drops are not credible. Alternatively, the protocol can restore commitment by decentralizing issuance, and this highlights a new benefit of DeFi protocols. This paper was accepted by Will Cong, finance. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2024.06992 .