There has been a large rise in savings by Americans in the top 1% of the income or wealth distribution over the past 35 years, which we call the saving glut of the rich. The saving glut of the rich has been almost as large as the global saving glut, and it has not been associated with an increase in investment. Instead, this rise in savings has been associated with substantial dissaving by the non-rich and dissaving by the government. A process by which the financial sector is unveiled reveals that rich households have accumulated substantial financial assets that are direct claims on household and government debt. Analysis using variation across states shows that the rise in top income shares has been important in generating the saving glut of the rich.