This paper studies how quantitative easing (QE) affects household welfare across the wealth distribution. I build a Heterogeneous Agent New Keynesian (HANK) model with household portfolio choice, wage and price rigidities, endogenous unemployment, frictional financial intermediation, an effective lower bound (ELB) on the policy rate, forward guidance, and QE. To quantify the contribution of the various channels through which monetary policy affects inequality, I estimate the model using Bayesian methods, explicitly taking into account the occasionally binding ELB constraint and the QE operations undertaken by the Federal Reserve during the 2009-15 period. I find that the QE program unambiguously benefited all households by stimulating economic activity. However, it had nonlinear distributional effects. On the one hand, it widened the income and consumption gap between the top 10 percent and the rest of the wealth distribution by boosting profits and equity prices. On the other hand, QE shrank inequality within the lower 90 percent of the wealth distribution, primarily by lowering unemployment. On net, it reduced overall wealth and income inequality, as measured by the Gini index. Surprisingly, QE has weaker distributional consequences compared with conventional monetary policy. Lastly, forward guidance and an extended period of zero policy rates amplified both the aggregate and the distributional effects of QE.