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Using the fact that multiple elementary schools feed into the same middle school, I demonstrate that the positive impact that teachers have on their own students spills over to affect their students' future peers. Although this indirect effect on any particular individual is small a teacher impacts many more students indirectly than directly, so the indirect value is a sizable portion of a teacher's total value; I find that ignoring teachers' indirect effects underestimates their value by roughly 35%. Because the spillovers also affect teacher value added estimates, I develop a method of moments estimator of teacher value added that accounts for the spillovers and show that accounting for the spillovers does not have a large impact on the ranking of teachers in New York City. I conclude by showing that the spillovers occur within groups of students who share the same race and gender, which highlights the crucial importance that the social network plays in disseminating the effect.