  We present an analytical strong-disorder renormalization group theory of the
quantum phase transition in the dissipative random transverse-field Ising
chain. For Ohmic dissipation, we solve the renormalization flow equations
analytically, yielding asymptotically exact results for the low-temperature
properties of the system. We find that the interplay between quantum
fluctuations and Ohmic dissipation destroys the quantum critical point by
smearing. We also determine the phase diagram and the behavior of observables
in the vicinity of the smeared quantum phase transition.
