We develop a multi-sector New Keynesian model to analyze the inflationary effects of climate policies. Climate policies need not be inflationary, but can generate an inflation-output tradeoff whose size depends on the relative flexibility of “dirty” sectors prices vis-à-vis the rest of the economy. A version of the model calibrated to U.S. input-output data and sectoral heterogeneity in emissions and price stickiness matches the empirical responses to an energy shock of various CPI indexes well. It suggests that carbon taxes would have sizable inflationary implications if accommodated, while containing their impact on inflation would lead to a prolonged contraction.