This paper introduces a proposal for money market fund (MMF) reform to mitigate the systemic risk and externalities that arise from the funds' vulnerability to runs and to protect shareholders who do not redeem quickly when runs occur. Our proposal would require that a small fraction of each MMF shareholder's recent balances, called the "minimum balance at risk" (MBR), be available for redemption only with a delay of 30 days. Most regular transactions in the fund would be unaffected; the requirement would only affect redemptions of the shareholder's MBR. In addition, in the rare event that a fund suffers losses, the MBRs of investors who have recently made large redemptions would absorb losses before those of nonredeeming investors. This subordination of redeeming investors' MBRs would create a disincentive to redeem if the fund is likely to have losses, but would have little effect on incentives when the risk of loss is remote. We use empirical evidence, including a novel data set from the U.S. Treasury and the U.S. Securities and Exchange Commission on MMF losses in 2008, to calibrate an MBR rule that would reduce the vulnerability of MMFs to runs.