  Let $G$ be a complex simply connected semisimple Lie group and let $\Gamma$
be a torsionless uniform irreducible lattice in $G$. Then $\Gamma\backslash G$
is a compact complex non-K\"ahler manifold whose tangent bundle is
holomorphically trivial. In this note we compute the Picard group of
$\Gamma\backslash G$ when $\rank(G)\geq 3$. When $\rank(G)\lneq 3$, we
determine the group $Pic^0(\Gamma\backslash G)\subset Pic(\Gamma\backslash G)$
of topologically trivial holomorphic line bundles.
  When $\rank(G)\ge 2$, we also show that $Pic^0(P_\Gamma)$ is isomorphic to
$Pic^0(Y)$ where $P_\Gamma$ is a $\Gamma\backslash G$-bundle associated to a
principal $G$-bundle over a compact connected complex manifold $Y$, and, when
$\rank(G)\ge 3$, we show that $Pic(Y)\to Pic(P_\Gamma)$ is injective with
finite cokernel.
