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.PACS numbers: 76.50.+g,78.20.Ls,78.20.Bh,78.70.Gq Collective excitations of spins in magnets, so-called magnons or spin waves, can be activated not only via a direct process with ac magnetic field H ω coupled to magnetizations but also via an electric excitation by ac electric field E ω coupled to charge degrees of freedom. When the magnon or spin-wave modes have simultaneous activity to the H ω and E ω components of electromagnetic waves, interference between the two activation processes, that is, the magnetically activating and the electrically activating processes, gives rise to peculiar optical and/or microwave phenomena, so-called optical ME effect. One of the most important examples is the directional dichroism, that is, oppositely propagating electromagnetic waves exhibit different absorptions.Multiferroic materials with concurrent magnetic and ferroelectric orders [1][2][3][4][5][6][7][8] provide an opportunity to realize the electric-dipole active magnons (so-called electromagnons) [9][10][11][12][13], and thus the optical ME effect via the magnetoelectric coupling [14][15][16]. Indeed observations of the directional dichroism have been reported for several multiferroic materials such as Ba 2 CoGe 2 O 7 [17][18][19], RMnO 3 (R =rare-earth ions) [20,21], and CuFe 1−x Ga x O 2 [22], in which nontrivial spin orders induce the ferroelectric polarization via the relativistic spin-orbit interaction. In these materials, the optical ME effect is observed at the electromagnon resonance frequencies in the terahertz (THz) regime.The directional dichroism is observed also at higher frequencies, i.e., x-ray and visible-light regimes in several polar magnets, which is caused by electron transitions among the spin-orbit multiplets [23][24][25][26][27][28][29]. However, observations of the effect at gigahertz (GHz) frequencies are quite limited and the effect observed so far is very tiny whose difference in absorption intensity is only 2.5% at most [32], while the directional dichroism at GHz frequencies is anticipated for application to microwave devices [30]. This is because most of the well-known multiferroic materials based on simple spiral or antiferromagnetic spin structures with short-period modulation tend to have relatively large spin-wave gaps of several meV, which inevitably results in rather high resonance frequencies in THz regime. To achieve the microwave ME effect...