  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 $\sin^2\theta_{e4}
\sim 10^{-7}$ / $\rm m_{^{163}\rm Dy}\rm{(ton)}$ could possibly be explored
with a real-time experiment.
