  We study the properties of the normal modes of a chain of Josephson junctions
in the simultaneous presence of disorder and absorption. We consider the
superconducting regime of small phase fluctuations and focus on the case where
the effects of disorder and absorption can be treated additively. We analyze
the frequency shift and the localization length of the modes. We also calculate
the distribution of the frequency-dependent impedance of the chain. The
distribution is Gaussian if the localization length is long compared to the
absorption length; it has a power law tail in the opposite limit.
