Mass transfer in stellar binaries has been well studied in most stellar mass ranges, with the notable exception of ultracool stars and substellar brown dwarfs. We report the discovery of ZTF J1239+8347 with the Zwicky Transient Facility (ZTF), a brown dwarf binary currently undergoing stable mass transfer with an orbital period of 57.41 minutes. Optical time-series photometry reveals an extremely high amplitude (>2 magnitude peak-to-trough) variability at short wavelengths, indicative of an orbiting hot spot slightly buried inside the atmosphere of the accretor. We use parallax measurements from Gaia along with optical and near-infrared spectra to infer an accretion temperature of Teff = 8904 ± 54 K, an atmospheric temperature of the accretor of Tatmo ≍ 1500 K, and a slightly inflated accretor radius of Racc=1.20−0.11+0.15RJup . ZTF J1239+8347 is a direct impact accretor, typically only seen in double degenerate white dwarf binaries, which are approximately a million times denser than the components in ZTF J1239+8347. The existence of an accreting brown dwarf binary suggests that angular momentum loss can be strong enough to make ultracool binaries interact in a Hubble time. The observed faintness (∼20 mag) and relative proximity (≍300 pc) of ZTF J1239+8347 suggest that many similar systems are likely to be found by the upcoming Rubin Observatory Legacy Survey of Space and Time.