  Let $U_m$ be an $m \times m$ Haar unitary matrix and $U_{[m,n]}$ be its $n
\times n$ truncation. In this paper the large deviation is proven for the
empirical eigenvalue density of $U_{[m,n]}$ as $m/n \to \lambda $ and $n \to
\infty$. The rate function and the limit distribution are given explicitly.
$U_{[m,n]}$ is the random matrix model of $quq$, where $u$ is a Haar unitary in
a finite von Neumann algebra, $q$ is a certain projection and they are free.
The limit distribution coincides with the Brown measure of the operator $quq$.
