Ultracool dwarfs (UCDs) are a category of astronomical objects that includes brown dwarfs and very-low-mass stars. Radio observations of UCDs have measured their brightness as a function of time (light curves) and spectral energy distributions, providing insight into their magnetic fields. We present spatially resolved radio observations of the brown dwarf LSR J1835+3259 using very-long-baseline interferometry showing extended radio emission. The detected morphology is consistent with the presence of a radiation belt. Comparison with models indicates that the radiation belt contains energetic particles confined by magnetic mirroring. We contend that radio-emitting UCDs have dipole-ordered magnetic fields with radiation belt-like morphologies and aurorae that are similar to those of Jupiter.