The simultaneous existence and coupling of ferroelectric and magnetic ordering in a material, so-called multiferroicity, is of great scientific interest due to the underlying complex physical mechanisms and its possible applications. Here we present the multiferroic properties of a prototypical spin-driven ferroelectric material, the spin-1/2 chain cuprate LiCuVO4. In this system, spiral spin order, with propagation in the b direction and a spin helix in the ab plane, induces ferroelectric polarization in the a direction when no magnetic field is applied. In an external magnetic field, the direction of the spin spiral and thus the direction of the electrical polarization can be switched. Broadband dielectric spectroscopy on a single crystalline sample oriented in two different directions was performed in applied external magnetic fields up to 9 T, demonstrating this switching behaviour of the ferroelectric polarization. Furthermore, detailed magnetic-field and temperature-dependent ferroelectric hysteresis-loop measurements reveal the switching of polarization by an electrical field, which implies the electric control of the spin helicity of LiCuVO4.