We theoretically find that in a multiferroic chiral magnet Cu2OSeO3, resonant magnetic excitations are coupled to collective oscillation of electric polarization, and thereby attain simultaneous activity to ac magnetic field and ac electric field. Because of interference between these magnetic and electric activation processes, this material hosts gigantic magnetochiral dichroism on microwaves, that is, the directional dichroism at gigahertz frequencies in Faraday geometry. The absorption intensity of microwave differs by as much as 30% depending on whether its propagation direction is parallel or antiparallel to the external magnetic field.