  It is well-known that chiral anomaly can be macroscopically detected through
the energy and charge transport, due to the chiral magnetic effect. On the
other hand, in a holographic many body system, the chaotic modes might be only
associated with the energy conservation. This suggests that, perhaps, one can
detect microscopic anomalies through the diagnosis of quantum chaos in such
systems. To investigate this idea, we consider a magnetized brane in AdS space
time with a Chern-Simons coupling in the bulk. By studying the shock wave
geometry in this background, we first compute the corresponding butterfly
velocities, in the presence of an external magnetic field $B$, in $\mu\ll T$
and $ B \ll T^2$ limit. We find that the butterfly propagation in the direction
of $B$ has a different velocity than in the opposite direction. The splitting
of butterfly velocities confirms the idea that chiral anomaly can be
macroscopically manifested via quantum chaos. We then show that the
pole-skipping points of energy density Green's function of the boundary theory
coincide precisely with the chaos points. This might be regarded as the
hydrodynamic origin of quantum chaos in an anomalous system. Additionally, by
studying the near horizon dynamics of a scalar field on the above background,
we find the spectrum of pole-skipping points associated with the two-point
function of dual boundary operator. We find that the sum of wavenumbers
corresponding to pole-skipping points at a specific Matsubara frequency is a
universal quantity, which is independent of the scaling dimension of the dual
boundary operator. We then show that this quantity follows from a closed
formula and can be regarded as another macroscopic manifestation of the chiral
anomaly.
