We report the discovery of a ferroelectric ground state below 4.5 K in highly underdoped La_2CuO_(4+x) accompanied by slow charge dynamics which develop below T~40 K. An anisotropic magnetoelectric response has also been observed, indicating considerable spin-charge coupling in this lightly doped parent high temperature copper-oxide superconductor. The ferroelectric state is proposed to develop from polar nanoregions, in which spatial inversion symmetry is locally broken due to non-stoichiometric carrier doping.