The heated debate about how to reform Social Security has come to a standstill because the view of most Democrats (that Social Security must be a defined benefits plan similar in spirit to the current system) seems irreconcilable with the proposals supported by many Republicans (to create a defined contribution system of personal accounts holding marketed assets). We describe a system of “progressive personal accounts” that preserves the core goals of both parties, and that is self-balancing on an ongoing basis. Progressive personal accounts have two critical features: (1) accruals into the personal accounts would be exclusively in a new kind of derivative security (which we call a PAAW for Personal Annuitized Average Wage security) that pays its owner one inflation-corrected dollar during every year of life after his statutory retirement date, multiplied by the economy wide average wage at the retirement date and (2) households would buy their new PAAWs each year with their social security contributions, augmented or reduced by a government match that would add to contributions from households with low lifetime incomes by taking from households with high lifetime incomes. PAAWS define benefits and achieve risk sharing across generations, as Democrats would like, yet can be held in personal accounts with market valuations, as Republicans propose.