  An exact and explicit ladder-tensor-network ansatz is presented for the
non-equilibrium steady state of an anisotropic Heisenberg XXZ spin-1/2 chain
which is driven far from equilibrium with a pair of Lindblad operators acting
on the edges of the chain only. We show that the steady-state density operator
of a finite system of size n is - apart from a normalization constant - a
polynomial of degree 2n-2 in the coupling constant. Efficient computation of
physical observables is faciliated in terms of a transfer operator reminiscent
of a classical Markov process. In the isotropic case we find cosine spin
profiles, 1/n^2 scaling of the spin current, and long-range correlations in the
steady state. This is a fully nonperturbative extension of a recent result
[Phys. Rev. Lett. 106, 217206 (2011)].
