  In this paper we study almost complex manifolds admitting a quasi-K\"ahler
Chern-flat metric (Chern-flat means that the holonomy of the Chern connection
is trivial). We prove that in the compact case such manifolds are all
nilmanifolds. Some partial classification results are established and we prove
that a quasi-K\"ahler Chern-flat structure can be tamed by a symplectic form if
and only if the ambient space is isomorphic to a flat torus.
