  To study the effect of parity-violation on the rate of complexity growth, by
using "Complexity=Action" conjecture, we find the complexity growth rates in
different solutions of the chiral theory of Topologically Massive Gravity (TMG)
and parity-preserving theory of New Massive Gravity (NMG). Using the results,
one can see that decreasing the parameter $\mu$, which increases the effect of
Chern-Simons term and increases chirality, would increase the rate of growth of
complexity. Also one can observe a stronger correlation between complexity
growth and temperature rather than complexity growth and entropy. At the end we
comment on the possible meaning of the deforming term of chiral Liouville
action for the rate of complexity growth of warped CFTs in the Tensor Network
Renormalization picture.
