We have studied the magnetic structure of the ferroelectric frustrated spin-1/2 chain material LiCuVO4 in applied electric and magnetic fields using polarized neutrons. A symmetry and mean-field analysis of the data rules out the presence of static Dzyaloshinskii-Moriya interaction, while exchange striction is shown to be negligible by our specific-heat measurements. The experimentally observed magnetoelectric coupling is in excellent agreement with the predictions of a purely electronic mechanism based on spin supercurrents.