The behavior of liquid water under an electric field is a crucial phenomenon in science and engineering. However, its detailed description at a microscopic level is difficult to achieve experimentally. Here we report on the first ab initio molecular-dynamics study on water under an electric field. We observe that the hydrogen-bond length and the molecular orientation are significantly modified at low-to-moderate field intensities. Fields beyond a threshold of about 0.35 V/Å are able to dissociate molecules and sustain an ionic current via a series of correlated proton jumps. Upon applying even more intense fields (~1.0 V/Å), a 15%-20% fraction of molecules are instantaneously dissociated and the resulting ionic flow yields a conductance of about 7.8 W-1cm-1, in good agreement with experimental values. This result paves the way to quantum-accurate microscopic studies of the effect of electric fields on aqueous solutions and, thus, to massive applications of ab initio molecular dynamics in neurobiology, electrochemistry, and hydrogen economy.