The long-range ordering of magnetic and/or electric dipoles are canonical causes of phase transitions in crystalline materials, and they are both associated with a variety of functional properties. In addition to ferromagnetism, known as a property of the mineral magnetite since ancient times, and antiferromagnetism, first predicted theoretically in 1948 and soon after confirmed experimentally by neutron diffraction, many types of non-collinear magnetic ordering are known, such as those in which magnetic dipoles rotate describing helical patterns. By contrast, only parallel (ferroelectric) and antiparallel (antiferroelectric) alignments of electric dipoles have thus far been reported. This gives rise to a natural question; are there electric-dipole counterparts to the most complex magnetic structures found to date? Nearly sixty years after the discovery of helical magnetism, we describe the first example of incommensurate helical ordering of electric dipoles in the lightly-doped perovskite BiCu_{x}Mn_{7-x}O_{12}, thus completing the analogy between ordering of magnetic and electric dipoles. In a remarkable similarity to the phenomenon of spin-driven ferroelectricity found in prototypical multiferroics that support helical magnetic structures, structural chirality associated with the helical dipole texture in BiCu_{x}Mn_{7-x}O_{12} also couples to an improper macroscopic polarization. This opens a unique paradigm for the control of chiral domains and their optical activity by an applied electric field.