We report the discovery of ferroelectricity below 4.5 K in highly underdoped La₂CuO_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 nonstoichiometric carrier doping. Phys. Rev. B 85, 214502, 2012.