We investigate a new method to search for keV-scale sterile neutrinos that could account for Dark Matter. Neutrinos trapped in our galaxy could be captured on stable ${}^{163}$Dy if their mass is greater than 2.83 keV. Two experimental realizations are studied, an integral counting of ${}^{163}$Ho atoms in dysprosium-rich ores and a real-time measurement of the emerging electron spectrum in a dysprosium-based detector. The capture rates are compared to the solar neutrino and radioactive backgrounds. An integral counting experiment using several kilograms of ${}^{163}$Dy could reach a sensitivity for the sterile-to-active mixing angle $\sin^2\theta_{e4}$ of $10^{-5}$ significantly exceeding current laboratory limits. Mixing angles as low as $\sin^2\theta_{e4} \sim 10^{-7} /{\rm m_{{}^{163}Dy} (ton)}$ could possibly be explored with a real-time experiment.
