Self-charging of a solid tritium film (T2) has been discovered by chance in a precision β spectroscopy experiment on tritium β decay as a shift of the endpoint energy by several eV. The effect was then investigated systematically as a function of film thickness and time by measuring the energy shift of monochromatic conversion electrons from 83 m Kr evaporated onto T2 films. The steady state is characterized by a practically constant, critical electric field strength E c ≈62 MV/m (≈20 mV/monolayer) over the film, at which the residual positive charges attain sufficient mobility to penetrate the film towards the conducting substrate. This kind of breakthrough behaviour is analyzed in terms of a thermal hopping model, where a trapping potential of Φ 0≈175 k BK is lowered in direction of the electric force by a factor of 3 in order to facilitate hopping at a film temperature of about 1.9 K.