  In this note we explore the validity of the first law of entanglement entropy
in the context of the topologically massive gravity (TMG). We found that the
variation of the holographic entanglement entropy under perturbation from the
pure AdS background satisfies the first law upon imposing the bulk equations of
motion in a given time slice, despite the appearance of instabilities in the
bulk for generic gravitationl Chern-Simons coupling $\mu$. The black hole
entropy is different from the holographic entanglement entropy in a general
boosted frame. This discrepancy however do not affect the entanglement first
law.
