  The phonon magnetochiral effect consists of a nonreciprocity in the velocity
or attenuation of acoustic waves when they propagate parallel and antiparallel
to an external magnetic field. The first experimental observation of this
effect has been reported recently in a chiral magnet and ascribed to the
hybridization between acoustic phonons and chiral magnons. Here, we predict a
potentially measurable phonon magnetochiral effect of electronic origin in
chiral Weyl semimetals. Caused by the Berry curvature and the orbital magnetic
moment, this effect is enhanced for longitudinal phonons by the chiral anomaly.
