We show that the D^- meson will form narrow bound states with ^{208}Pb. Mean field potentials for the D^0, D^0-bar and D^- in ^{208}Pb are calculated self-consistently using the quark-meson coupling (QMC) model in local density approximation. The meson-^{208}Pb bound state energies are then calculated by solving the Klein-Gordon equation with these potentials. The experimental confirmation and comparison with the D^0-bar and D^0 will provide distinctive information on the nature of the interaction between the charmed meson and matter.