  We study the influence of Ohmic dissipation on the random transverse-field
Ising chain by means of large-scale Monte-Carlo simulations. To this end, we
first map the Hamiltonian onto a classical Ising model with long-range
$1/\tau^2$ interaction in the time-like direction. We then apply the highly
efficient cluster algorithm proposed by Luijten and Bl\"ote for system with
long-range interactions. Our simulations show that Ohmic dissipation destroys
the infinite-randomness quantum critical point of the dissipationless system.
Instead, the quantum phase transition between the paramagnetic and
ferromagnetic phases is smeared. We compare our results to recent predictions
of a strong-disorder renormalization group approach, and we discuss
generalizations to higher dimensions as well as experiments.
