  In the present paper, we consider the Chern-Simons-Schr\"{o}dinger system
\begin{equation} \left\{ \begin{aligned} &-\varepsilon^{2}\Delta
u+V(x)u+(A_{0}+A_{1}^{2}+A_{2}^{2})u=|u|^{p-2}u,\,\,\,\,x\in \mathbb{R}^2,\\
&\partial_1 A_0 = A_2 u^2,\ \partial_{2}A_{0}=-A_{1}u^{2},\\
&\partial_{1}A_{2}-\partial_{2}A_{1}=-\frac{1}{2}|u|^{2},\
\partial_{1}A_{1}+\partial_{2}A_{2}=0,\\ \end{aligned} \right. \end{equation}
where $p>2,$ $\varepsilon>0$ is a parameter and
$V:\mathbb{R}^{2}\rightarrow\mathbb{R}$ is a bounded continuous function. Under
some mild assumptions on $V(x)$, we show the existence and local uniqueness of
positive multi-peak solutions. Our methods mainly use the finite dimensional
reduction method, various local Pohozaev identities, blow-up analysis and the
maximum principle. Because of the nonlocal terms involved by $A_{0},A_{1}$ and
$A_{2},$ we have to obtain a series of new and technical estimates.
