  Given a non compact semisimple Lie group $G$ we describe all homogeneous
spaces $G/L$ carrying an invariant almost K\"ahler structure $(\omega,J)$. When
$L$ is abelian and $G$ is of classical type, we classify all such spaces which
are Chern-Einstein, i.e. which satisfy $\rho = \lambda\omega$ for some
$\lambda\in\mathbb R$, where $\rho$ is the Ricci form associated to the Chern
connection.
