Vector-chiral (VC) antiferromagnetism is a spiral-like ordering of spins which may allow ferroelectricity to occur due to loss of space inversion symmetry. In this Letter we report direct experimental observation of ferroelectricity in the VC phase of beta-TeVO4, a frustrated spin chain system with pronounced magnetic anisotropy and a rich phase diagram. Saturation polarization is proportional to neutron scattering intensities that correspond to the VC magnetic reflection. This implies that an inverse Dzyaloshinskii-Moriya mechanism is responsible for driving electric polarization. Linear magnetoelectric coupling is absent; however an unprecedented dependence of electric coercive field on applied magnetic field reveals a distinct way of manipulating multiferroic information.