We experimentally demonstrate one-way transparency of light in multiferroic CuB(2)O(4). The material is rendered transparent for light propagating in one direction, while opaque for light propagating in the opposite direction. The novel transparency results from a destructive interference of the electric dipole and magnetic dipole transitions. The realization of the effect has been accomplished by the application of a high magnetic field and the proper selection of the propagation direction of light in agreement with our quantum mechanical formulation of nonreciprocal directional dichroism.