  We study theoretically the transport through a single impurity in a
one-channel Luttinger liquid coupled to a dissipative (ohmic) bath . For
non-zero dissipation $\eta$ the weak link is always a relevant perturbation
which suppresses transport strongly. At zero temperature the current voltage
relation of the link is $I\sim \exp(-E_0/eV)$ where $E_0\sim\eta/\kappa$ and
$\kappa$ denotes the compressibility. At non-zero temperature $T$ the linear
conductance is proportional to $\exp(-\sqrt{{\cal C}E_0/k_BT})$. The decay of
Friedel oscillation saturates for distance larger than $L_{\eta}\sim 1/\eta $
from the impurity.
