We propose a supply-side channel for the transmission of monetary policy. We show that in an economy with heterogeneous firms and endogenous markups, monetary shocks have first-order effects on aggregate productivity. If high-markup firms have lower pass-throughs than lowmarkup firms, as is consistent with the empirical evidence, then a monetary easing generates an endogenous positive "supply shock" that amplifies the positive "demand shock" on output. 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 derive a tractable fourequation dynamic model, disciplined by four sufficient statistics from the distribution of firms, and use it to show that a monetary easing generates a procyclical hump-shaped response in aggregate TFP and countercyclical dispersion in firm-level TFPR. In the data, in line with the model's predictions, we observe both procyclical aggregate productivity and reallocations to high-markup firms during expansions. A calibration using firm-level pass-throughs suggests that the supply-side channel is quantitatively as important as real rigidities, and amplifies both the impact and persistence of monetary shocks. Moreover, this channel becomes stronger, and the Phillips curve becomes flatter, with increases in industrial concentration.