  In the present paper, we consider the following magnetic nonlinear Choquard
equation $$ \left\{
  \begin{array}{ll}
  & (-i \nabla+A(x))^2u + \mu g(x)u = \lambda u + (|x|^{-\alpha} *
|u|^{2^*_\alpha})|u|^{2^*_\alpha-2}u ,\; u>0 \;\text{in} \; \mathbb{ R}^n ,
  & u \in H^1(\mathbb{R}^n, \mathbb{ C})
  \end{array} \right\}.$$ where $n \geq 4$, $2^*_\alpha=
\frac{2n-\alpha}{n-2}$, $\lambda>0$, $\mu \in \mathbb{ R}$ is a parameter,
$\alpha \in (0,n)$, $A(x): \mathbb{R}^n \rightarrow \mathbb{ R}^n$ is a
magnetic vector potential and $g(x)$ is a real valued potential function on
$\mathbb{R}^n$. Using variational methods, we establish the existence of least
energy solution under some suitable conditions. Moreover, the concentration
behavior of solutions is also studied as $\mu \rightarrow +\infty$.
