This paper studies the transmission of US monetary policy shocks into Emerging Markets emphasizing the role of investment and financial heterogeneity. First, we use a panel SVAR model to show that a US interest tightening leads to a persistent recession in Emerging Markets driven by a sharp reduction in aggregate investment. Second, we study the role of firms' financial heterogeneity in the transmission of US interest rate shocks by exploiting detailed balance sheet dataset from Chile. We find that more indebted firms experience greater drops in investment in response to a US tightening shock than less indebted firms. This result is at odds with recent evidence from US firms, even when using the same identification strategy and econometric methods. Third, we rationalize this finding using a stylized model of heterogeneous firms subject to a tightening leverage constraint. Finally, we present evidence in support of this hypothesis as well as robustness checks to our main results. Overall, our results suggests that the transmission channel of US monetary policy shocks within and outside the US differ, a result novel to the literature.