We report on the neutral-to-ionic (N-I) phase transition in the one-dimensional organic complex (BEDT-TTF)-(ClMeTCNQ). The X-ray studies at room temperature show that the neutral phase of (BEDT-TTF)-(ClMeTCNQ) is already characterized by a polar long-range ordering, at variance with other charge-transfer compounds comprising noncentrosymmetric molecules. From a detailed neutron diffraction study of this complex under high pressure, we present the phase diagram of the N-I transition down to the quantum limit. We discuss the symmetry breaking associated with the transition and the evolution of its first-order character under pressure.