  It is shown theoretically that the Luttinger liquid phase in
quasi-one-dimensional conductors can exist in the presence of impurities in a
form of a collection of bounded Luttinger liquids. The conclusion is based upon
the observation by Kane and Fisher that a local impurity potential in Luttinger
liquid acts, at low energies, as an infinite barrier. This leads to a discrete
spectrum of collective charge and spin density fluctuations, so that interchain
hopping can be considered as a small parameter at temperatures below the
minimum excitation energy of the collective modes. The results are compared
with recent experimental observation of a Luttinger-liquid-like behavior in
thin NbSe$_3$ and TaS$_3$ wires.
