Electrocorticography uses non-penetrating electrodes embedded in flexible substrates to record electrical activity from the surface of the brain. To use the technology to develop minimally invasive, high-bandwidth brain–computer interfaces, it will be necessary to improve the number of recording channels and the scalability of devices, which could be achieved by merging electrodes and electronics onto a single substrate. Here we report a 50-μm-thick, mechanically flexible micro-electrocorticography brain–computer interface that integrates a 256 × 256 array of electrodes, signal processing, data telemetry and wireless powering on a single complementary metal–oxide–semiconductor substrate. The device contains 65,536 recording electrodes, from which we can simultaneously record a selectable subset of up to 1,024 channels at a given time. Our chip is wirelessly powered, and when implanted below the dura, it can communicate bidirectionally with an external relay station outside the body. We show that the device can provide chronic, reliable recordings for up to two weeks in pigs and up to two months in behaving non-human primates from the somatosensory, motor and visual cortices, decoding brain signals at high spatiotemporal resolution.