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Spin waves represent the collective excitations of the magnetization field within a magnetic material, providing dispersion curves that can be manipulated by material design and external stimuli. Bulk and surface spin waves can be excited in a thin film with positive or negative group velocities and, by incorporating a symmetry-breaking mechanism, magnetochiral features arise. Here we study the band diagram of a chiral magnonic crystal consisting of a ferromagnetic film incorporating a periodic Dzyaloshinskii–Moriya coupling via interfacial contact with an array of heavy-metal nanowires. We provide experimental evidence for a strong asymmetry of the spin wave amplitude induced by the modulated interfacial Dzyaloshinskii–Moriya interaction, which generates a nonreciprocal propagation. Moreover, we observe the formation of flat spin-wave bands at low frequencies in the band diagram. Calculations reveal that …