How strong are strategic complementarities in price setting across firms? In this paper, we provide a direct empirical estimate of firms' price responses to changes in prices of their competitors. We develop a general framework and an empirical identification strategy to estimate the elasticities of a firm's price response both to its own cost shocks and to the price changes of its competitors. Our approach takes advantage of a new micro-level data set for the Belgian manufacturing sector, which contains detailed information on firm domestic prices, marginal costs, and competitor prices. The rare features of these data enable us to construct instrumental variables to address the simultaneity of price setting by competing firms. We find strong evidence of strategic complementarities, with a typical firm adjusting its price with an elasticity of 35 percent in response to the price changes of its competitors and with an elasticity of 65 percent in response to its own cost shocks. Furthermore, we find substantial heterogeneity in these elasticities across firms, with small firms showing no strategic complementarities and a complete cost pass-through, and large firms responding to their cost shocks and competitor price changes with roughly equal elasticities of around 50 percent. We show, using a tightly calibrated quantitative model, that these findings have important implications for shaping the response of domestic prices to international shocks.