We study optimal monetary policy in an analytically tractable Heterogeneous Agent New Keynesian model with rich cross-sectional heterogeneity. Optimal policy differs from that in a representative agent model because monetary policy can affect consumption inequality, both by reducing idiosyncratic consumption risk and by reducing inequality arising from households' unequal exposures to aggregate shocks. Simple target criteria summarize the planner's trade-off between consumption inequality, productive efficiency and price stability. Mitigating consumption inequality requires putting some weight on stabilizing the level of output, and correspondingly reducing the weights on the output gap and the price level relative to an economy without inequality.