We use a near-representative household panel survey of ∼19,000 primary-school-aged children in rural Tamil Nadu to study the extent of ‘learning loss’ after COVID-19 school closures, the pace of recovery in the months after schools reopened, and the role of a flagship compensatory intervention introduced by the state government. Students tested in December 2021, after 18 months of school closures, displayed severe deficits in learning of about 0.7 standard deviations (σ) in math and 0.34σ in language compared to identically-aged students in the same villages in 2019. Using multiple rounds of in-person testing, we find that two-thirds of this deficit was made up in the 6 months after school reopening. Using value-added models, we attribute ∼24% of the cohort-level recovery to a government-run after-school remediation program which improved test scores for attendees by 0.17σ in math and 0.09σ in Tamil after 3-4 months. Further, while learning loss was regressive, the recovery was progressive, likely reflecting (in part) the greater take up of the remediation program by more socioeconomically disadvantaged students. These positive results from a state-wide program delivered at scale by the government may provide a useful template for both recovery from COVID-19 learning losses, and bridging learning gaps more generally in low-and-middle-income countries.