  We report results of low-temperature thermodynamic and transport measurements
of Pb_{1-x}Tl_{x}Te single crystals for Tl concentrations up to the solubility
limit of approximately x = 1.5%. For all doped samples, we observe a
low-temperature resistivity upturn that scales in magnitude with the Tl
concentration. The temperature and field dependence of this upturn are
consistent with a charge Kondo effect involving degenerate Tl valence states
differing by two electrons, with a characteristic Kondo temperature T_K ~ 6 K.
The observation of such an effect supports an electronic pairing mechanism for
superconductivity in this material and may account for the anomalously high T_c
values.
