Public debt and wealth concentration have co-moved persistently across advanced economies and historical periods, defying standard theories of wealth inequality, particularly given that rising inequality has coincided with falling real interest rates in recent decades. I develop a stylized Diamond model with household heterogeneity and progressive taxation to formalize how public debt, through its tax burden, endogenously dictates tax progressivity and thereby affects the wealth distribution. In this framework, permanent debt shocks alter tax progressivity depending on the macroeconomic regime, with debt expansions increasing progressivity when interest rates are high but reducing it when interest rates are low. The resulting impact of public debt on wealth inequality is nonlinear in the overall level of the tax burden, disequalizing below a threshold and equalizing above it. Cross-country empirical evidence supports these predictions and shows that public debt is a quantitatively important, and often dominant, driver of postwar wealth inequality, with sizable effects transmitted primarily through the tax burden. These findings establish the distribution of the tax burden as a primary driver of long-run wealth inequality, and public debt as a central mediating channel through which structural shocks, such as population aging or artificial intelligence, propagate to the wealth distribution.