Stablecoins promise a stable and secure way to park funds in the crypto universe. However, stablecoin issuers are vulnerable to runs triggered by negative information about the quality and liquidity of their reserves, as well as custodial, operational, and technological risks. I propose a framework for analyzing the factors influencing stablecoin adoption and fragility, which offers insights for risk assessment and appropriate regulation, as well as new testable implications. Under the premise that payment preferences are heterogeneous across potential stablecoin holders, a wider adoption of stablecoins is associated with a destabilizing composition effect. Positive network effects mitigate the destabilizing composition effect, but they may also undermine the role of bank deposits as a means of payment. The marginal stablecoin adopter does not internalize these effects. Consequently, adoption is likely to be excessive. Factors that increase the issuer's income from fees and seigniorage promote stability, as do congestion effects. A stablecoin lending market promotes both stability and adoption, if it is not undermined by speculation. The introduction of a moral hazard problem provides additional insights into reserve management and disclosure.