There has been a large rise in savings by Americans in the top 1% of the income or wealth distribution over the past 40 years, which we call the saving glut of the rich. Instead of financing investment, this saving glut has been associated with dissaving by the non-rich and dissaving by the government. An unveiling of the financial sector reveals that rich households have accumulated substantial financial assets that are direct claims on U.S. government and household debt. State-level analysis shows that the rise in top income shares has been important in generating the rise in savings by the rich.