The magnetochiral effect (MCE) of phonons, a nonreciprocal acoustic propagation arising due to symmetry principles, is demonstrated in the chiral-lattice ferrimagnet Cu2OSeO3. Our high-resolution ultrasound experiments reveal that the sound velocity differs for parallel and antiparallel propagation with respect to the external magnetic field. The sign of the nonreciprocity depends on the chirality of the crystal in accordance with the selection rule of the MCE. The nonreciprocity is enhanced below the magnetic ordering temperature and at higher ultrasound frequencies, which is quantitatively explained by a proposed magnon-phonon hybridization mechanism.