  We propose a mechanism to generate dissipationless current in time reversal
symmetry breaking Weyl semimetals through the anomalous chiral magnetic effect
(ACME). The ACME current is induced by chiral imbalance and flows along the
direction of the Weyl nodes separation in momentum space. In contrast to the
chiral magnetic effect, the ACME is not related to the chiral anomaly and does
not require external magnetic field. In the presence of parallel electric and
magnetic fields, the ACME gives rise to an antisymmetric linear
magnetoresistance and a planar Hall conductivity, which we estimate to be
observable.
