Hetero interfaces between metal-oxides display pronounced phenomena such as semiconductor-metal transitions, magnetoresistance, the quantum hall effect and superconductivity. Similar effects at compositionally homogeneous interfaces including ferroic domain walls are expected. Unlike hetero interfaces, domain walls can be created, displaced, annihilated and recreated inside a functioning device. Theory predicts the existence of 'strongly' charged domain walls that break polarization continuity, but are stable and conduct steadily through a quasi-two-dimensional electron gas. Here we show this phenomenon experimentally in charged domain walls of the prototypical ferroelectric BaTiO₃. Their steady metallic-type conductivity, 10(9) times that of the parent matrix, evidence the presence of stable degenerate electron gas, thus adding mobility to functional interfaces.