A self‐pinched relativistic electron beam is injected through a thin foil into vacuum with no externally applied magnetic field. The beam is observed to propagate at currents well above the space‐charge‐limiting current (∼3 kA) but limited to the Alfven current (∼30 kA). Propagation results from charge neutralization of the beam by ions accelerated out of the anode plasma as confirmed by various ion diagnostics. Ions are collectively accelerated to greater than the electron energy. The experimental results are in qualitative agreement with a one‐dimensional time‐dependent computer simulation.