The development of three-terminal superconducting devices with transistor-like characteristics may be crucial for a number of applications of superconducting electronics. A three-terminal Josephson device which in principle could have gain, and which depends on the magnetoelectric effect is described. The magnetoelectric effect is a property of the antiferromagnetic phase of certain compounds. When an electric field is applied across a magnetoelectric material, a magnetization develops. If one Josephson junction of a two-junction, three-electrode sandwich contained a magnetoelectric barrier, a magnetic field would result if that junction were switched to the finite voltage state. This field, when coupled into the second junction, would cause it to switch from the zero-voltage to the finite voltage state. If the second junction had a larger critical current than the drive junction, then the three-terminal device would have gain.