Despite the massive worldwide increase in school enrollment over the past 50 years, many students are not learning. Teacher quality—a key determinant of student achievement—remains low in many countries, and while governments invest heavily on teacher training programs, the evidence on their impact is inconclusive. Development economists, skeptical of teacher training, have instead largely focused on incentive programs. We present novel evidence on the impact of a national teacher coaching program in Peru using an at-scale randomized controlled trial. The program provided teachers in rural primary schools with individualized, continuous coaching on pedagogical practices. Coaching substantially improved learning: students in treatment schools experienced a 0.25-0.38 standard deviation increase in standardized test scores relative to the control group. The gains are observed throughout the test score distribution, with low-performing students benefitting as much as higher performing ones. Using a combination of experimental and non-experimental techniques to account for teacher rotation, we show that the program effects persist for at least one year after the training ends. Interestingly, the impact observed is entirely due to and retained by the trained teacher—schools that lose trained teachers lose the entire initial gains and, when treated teachers move, students benefit from the arrival of the trained teacher as much as students in the original school did. This suggests that the program is building up the human capital of teachers, rather than simply monitoring teacher presence or effort, and that this human capital is portable and persistent. Our results have important policy implications. We find that teacher training programs can indeed be impactful and cost-effective but, given the high level of teacher movement, individual schools may underinvest in teacher training thereby underscoring the need for public subsidies of such training.