We investigate the effect of dissipation on a small quantum dot (resonant level) tunnel coupled to a chiral Luttinger liquid (LL) with the LL parameter
K. The dissipation stems from the coupling of the dot to an electric environment, being characterized by the resistance
R, via Coulomb interactions. We show that this problem can be mapped onto a Caldeira-Leggett model where the (ohmic) bath of harmonic oscillators is governed by the effective dissipation strength $\ensuremath{\alpha}={(2\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K})}^{\ensuremath{-}1}$ with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{K}}^{\ensuremath{-}1}={K}^{\ensuremath{-}1}+2R∕{R}_{K}$ and
RK=h∕e2 the quantum of resistance. Experimental consequences are discussed and the limit
K=1∕2+ is thoroughly studied at small
R∕RK through the spin-boson-fermion model.