The electronic quality of two-dimensional systems is crucial when exploring quantum transport phenomena. In semiconductor heterostructures, decades of optimization have yielded record-quality two-dimensional gases with transport and quantum mobilities reaching close to 108 and 106 cm2 V−1 s−1, respectively1, 2, 3, 4, 5, 6, 7, 8, 9–10. Although the quality of graphene devices has also been improving, it remains comparatively lower11, 12, 13, 14, 15, 16–17. Here we report a transformative improvement in the electronic quality of graphene by employing graphite gates placed in its immediate proximity, at 1 nm separation. The resulting screening reduces charge inhomogeneity by two orders of magnitude, bringing it down to a few 107 cm−2 and limiting potential fluctuations to less than 1 meV. Quantum mobilities reach 107 cm2 V−1 s−1, surpassing those in the highest-quality semiconductor heterostructures by an order of magnitude, and the transport mobilities match their record9, 10. This quality enables Shubnikov–de Haas oscillations in fields as low as 1 mT and quantum Hall plateaux below 5 mT. Although proximity screening predictably suppresses electron–electron interactions, fractional quantum Hall states remain observable with their energy gaps reduced only by a factor of 3–5 compared with unscreened devices, demonstrating that many-body phenomena at spatial scales shorter than 10 nm remain robust. Our results offer a reliable route to improving electronic quality in graphene and other two-dimensional systems, which should facilitate the exploration of new physics previously obscured by disorder.