  We consider an $S=1/2$ antiferromagnetic quantum Heisenberg chain where each
site is coupled to an independent bosonic bath with ohmic dissipation. The
coupling to the bath preserves the global SO(3) spin symmetry. Using
large-scale, approximation-free quantum Monte Carlo simulations, we show that
any finite coupling to the bath suffices to stabilize long-range
antiferromagnetic order. This is in stark contrast to the isolated Heisenberg
chain where spontaneous breaking of the SO(3) symmetry is forbidden by the
Mermin-Wagner theorem. A linear spin-wave theory analysis confirms that the
memory of the bath and the concomitant retarded interaction stabilize the
order. For the Heisenberg chain, the ohmic bath is a marginal perturbation so
that exponentially large system sizes are required to observe long-range order
at small couplings. Below this length scale, our numerics is dominated by a
crossover regime where spin correlations show different power-law behaviors in
space and time. We discuss the experimental relevance of this crossover
phenomena.
