  In strong magnetic field the longitudinal magnetoconductivity in 3D chiral
materials is shown to exhibit a new type of quantum oscillations arising from
the chiral magnetic effect (CME). These quantum CME oscillations are predicted
to dominate over the Shubnikov-de Haas (SdH) ones in chiral materials with an
approximately conserved chirality of quasiparticles at strong magnetic fields.
The phase of quantum CME oscillations differs from the phase of the
conventional SdH oscillations by $\pi/2$.
