Materials with low thermal conductivity are important for a variety of applications such as thermal barrier coatings and thermoelectrics, and understanding the underlying mechanisms of low heat transport, as well as relating them to structural features, remains a central goal within material science. Here, we report on the ultralow thermal conductivity of the quarternary crystalline silver chalcogenide AgGaGe3Se8, with a remarkable value of only 0.2 watts per meter per kelvin at room temperature and an unusual glass-like thermal behavior from 2 to 700 kelvin. The ultralow thermal conductivity is linked to a disordered nature of silver in the structure, displaying extremely large silver atomic displacement parameters obtained from multitemperature synchrotron powder x-ray scattering measurements and silver ionic conductivity at elevated temperatures. In addition, a low-temperature Boson peak in the heat capacity and a low Debye temperature of 158 kelvin reveal signs of structural anharmonicity and soft bonding.