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Thermoelectric devices can directly convert waste heat into electricity, which makes them an important clean energy technology. The underlying materials performance can be evaluated by the dimensionless figure of merit ZT. Metal halides are attractive candidates due to their chemical flexibility and ease of processing; however, the maximum ZT realized (ZT=0.15) falls far below the level needed for commercialization (ZT>1). Using a first-principles procedure, we assess the thermoelectric potential of copper halide CsCu_{2}I_{3}, which features one-dimensional Cu-I connectivity. The n-type crystal is predicted to exhibit a maximum ZT of 2.2 at 600 K along the b axis. The strong phonon anharmonicity of this system is shown by locally stable noncentrosymmetric Amm2 structures that are averaged to form the observed centrosymmetric Cmcm space group. Our work provides insights into the structure-property relations in metal halide thermoelectrics and suggests a path forward to engineer higher-performance heat-to-electricity conversion.