  We compute one of the second order transport coefficients arising from the
chiral anomaly in a high temperature weakly coupled regime of quark-gluon
plasma. This transport coefficient is responsible for the CP-odd current that
is proportional to the time derivative of the magnetic field, and can be
considered as a first correction to the chiral magnetic conductivity at finite,
small frequency. We observe that this transport coefficient has a non-analytic
dependence on the coupling as $\sim 1/(g^4 \log(1/g))$ at weak coupling regime,
which necessitates a re-summation of infinite ladder diagrams with leading
pinch singularities to get a correct leading log result: a feature quite
similar to that one finds in the computation of electric conductivity. We
formulate and solve the relevant CP-odd Schwinger-Dyson equation in real-time
perturbation theory that reduces to a coupled set of second order differential
equations at leading log order. Our result for this second order transport
coefficient indicates that chiral magnetic current has some resistance to the
time change of magnetic field, which may be called "chiral induction effect".
We also discuss the case of color current induced by color magnetic field.
