In low-income countries, private schools are perceived as superior alternatives to the public sector, often improving achievement at a fraction of the cost. It is unclear whether private schools are as effective in middle-income countries where the public sector has relatively more resources. To address this gap, this paper takes advantage of lottery-based admissions in first grade for a Mexico City private school that targets and subsidizes attendance for low-income children. Over three years, selected students via lottery scored 0.21 standard deviation higher than those not selected in literacy tests, corresponding to a normalized gain of one-half of a grade level every two years. Lottery winners also statistically outperformed those not selected in math, but the gains were more modest. Relative to the control group, parents of selected students were more satisfied with their school and had higher educational expectations for their children. Unlike findings from low-income countries, these gains came at increased cost--twice as much on a per pupil basis relative to public schools. Additional analyses indicate gains made by the lowest income students in the sample help explain the school's impact. This suggests private schools could bring down persistent achievement gaps in these countries, but puts into question the validity of implementation at scale. [This paper is a product of the Education Global Practice.]