Electroporation, the application of electric fields to alter the permeability of biological membranes, has recently become a clinical tool for the electrochemotherapy treatment of various cancers. Current electroporation theory assumes that the membrane is permeabilized through the formation of conducting hydrophilic pores, stabilized by rearrangement of lipid head groups. Here we have performed molecular dynamics simulations of negatively charged lipid bilayers subject to high transmembrane voltages together with electroporation experiments on planar bilayers. Our data reveal a hitherto unknown electroporation process in which large ion-conducting water columns not stabilized by lipid head groups are formed within the bilayer's hydrophobic core. The existence of such hydrophobic pores challenges the standard theoretical description of pore creation in lipid membranes. Our findings open a new vista toward fine-tuning of electroporation-based treatments and biotechnical applications, and, in general, for enhancing the import of various substrates in liposomes or cells.