  In this article, we are study the following Dirichlet problem with Choquard
type non linearity \[ -\Delta_{\mathbb{H}} u = a u+
\left(\int_{\Omega}\frac{|u(\eta)|^{Q^*_\lambda}}{|\eta^{-1}\xi|^{\lambda}}d\eta\right)|u|^{Q^*_\lambda-2}u
\; \text{in}\; \Omega,\quad
  u = 0 \; \text{ on } \partial \Omega , \]
  where $\Omega$ is a smooth bounded subset of the Heisenberg group
$\mathbb{H}^N, N\in \mathbb N$ with $C^2$ boundary and $\Delta_{\mathbb{H}}$ is
the Kohn Laplacian on the Heisenberg group $\mathbb{H}^N$. Here,
$Q^*_\lambda=\frac{2Q-\lambda}{Q-2},\; Q= 2N+2$ and $a$ is a positive real
parameter. We derive the Brezis-Nirenberg type result for the above problem.
Moreover, we also prove the regularity of solutions and nonexistence of
solutions depending on the range of $a$.
