  Let $\pi$ be a $SL(3,\mathbb Z)$ Hecke-Maass cusp form satisfying the
Ramanujan conjecture and the Selberg-Ramanujan conjecture, and let $\chi$ be a
primitive Dirichlet character modulo $M$, which we assume to be prime for
simplicity. We will prove the following subconvex bound $$
L\left(\tfrac{1}{2},\pi\otimes\chi\right)\ll_{\pi,\varepsilon}
M^{\frac{3}{4}-\frac{1}{1612}+\varepsilon}. $$
