  We devise an autonomous quantum thermal machine consisting of three
pairwise-interacting qubits, two of which are locally coupled to separate
classical reservoirs. The machine operates autonomously, as it requires no
time-coherent control, external driving or quantum bath engineering, and is
instead propelled by a chemical potential bias between the reservoirs. Under
ideal conditions, we show that this out-of-equilibrium system can
deterministically generate a maximally entangled steady-state between two of
the qubits, or in fact, any desired pure two-qubit entangled state, emerging as
a dark state of the system. The entanglement production is also robust, such
that nearly-maximally-entangled states can be generated well-away from the
ideal regime of operation. Furthermore, we show that our machine architecture
can be generalised to a configuration with $2n-1$ qubits, in which only a
potential bias and two-body interactions are sufficient to generate genuine
multipartite maximally entangled steady states in the form of a W state of $n$
qubits.
