We study optimal monetary policy in an analytically tractable heterogeneous agent New Keynesian model with rich cross-sectional heterogeneity. Optimal policy differs from a representative agent benchmark because monetary policy can affect consumption inequality, by stabilizing consumption risk arising from both idiosyncratic shocks and unequal exposures to aggregate shocks. The trade-off between consumption inequality, productive efficiency, and price stability is summarized in a simple linear-quadratic problem yielding interpretable target criteria. Stabilizing consumption inequality requires putting some weight on stabilizing the level of output, and correspondingly reducing the weights on the output gap and price level relative to the representative agent benchmark.