  The emergence of chiral anomaly entails various fascinating phenomena such as
anomalous quantum Hall effect and chiral magnetic effect in different branches
of (non-)Hermitian physics. While in the single-particle picture, anomalous
currents merely appear due to the coupling of massless particles with
background fields, many-body interactions can also be responsible for anomalous
transport in interacting systems. In this Letter, we study anomalous chiral
currents in systems where interacting massless fermions with complex Fermi
velocities are coupled to complex gauge fields. Our results reveal that
incorporating non-Hermiticity and many-body interactions gives rise to
additional terms in anomalous relations beyond their Hermitian counterparts. We
further present that many-body corrections in the subsequent non-Hermitian
chiral magnetic field or anomalous Hall effect are nonvanishing in
nonequilibrium or inhomogeneous systems. Our results advance efforts in
understanding the anomalous transport in interacting non-Hermitian systems.
