We propose a supply-side channel for the transmission of monetary policy. We show that if, as is consistent with the empirical evidence, bigger firms have higher markups and lower pass-throughs than smaller firms, then a monetary easing endogenously increases aggregate TFP and improves allocative efficiency. This endogenous positive "supply shock" amplifies the effects of the positive "demand shock" on output and employment. The result is a flattening of the Phillips curve. This effect is distinct from another mechanism discussed at length in the real rigidities literature: a monetary easing leads to a reduction in desired markups because of strategic complementarities in pricing. We calibrate the model to match firm-level pass-throughs and find that the misallocation channel of monetary policy is quantitatively important, flattening the Phillips curve by about 70% compared to a model with no supply-side effects. We derive a tractable four-equation dynamic model and show that monetary easing generates a procyclical hump-shaped response in aggregate TFP and countercyclical dispersion in firm-level TFPR. The improvements in allocative efficiency amplify both the impact and persistence of interest rate shocks on output.