  In this article, we establish the existence of solutions to the following
critical Hartree equation \begin{align*} \begin{cases} -\Delta
u=\left(\int_{\Omega_\varepsilon}\frac{u^{2_{\mu}^*}}{|x-y|^{\mu}}dy\right)u^{2_{\mu}^*-1},
&\text{ in } \Omega_\varepsilon, \\ u=0, &\text{ on }
\partial\Omega_\varepsilon, \end{cases} \end{align*} where
$2_{\mu}^*=\frac{2N-\mu}{N-2}$ is the upper critical exponent in the sense of
the Hardy-Littlewood-Sobolev inequality, $N\geq 5$, $0<\mu<4$ with $\mu$
sufficiently close to $0$, $\Omega_\varepsilon:=\Omega\backslash
B(0,\varepsilon)$ and $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$,
which contains the origin, and $\varepsilon$ is a positive parameter. As
$\varepsilon$ goes to zero, we construct bubble solution which blows up at the
origin.
