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

Disordered Josephson junction chains: Anderson localization of normal modes and impedance fluctuations