VSe2 is a transition metal dichaclogenide which has a charge-density wave transition that has been well studied. We report on a low-temperature upturn in the resistivity and, at temperatures below this resistivity minimum, an unusual magnetoresistance which is negative at low fields and positive at higher fields, in single crystals of VSe2. The negative magnetoresistance has a parabolic dependence on the magnetic field and shows little angular dependence. The magnetoresistance at temperatures above the resistivity minimum is always positive. We interpret these results as signatures of the Kondo effect in VSe2. An upturn in the susceptibility indicates the presence of interlayer V ions which can provide the localized magnetic moments required for scattering the conduction electrons in the Kondo effect. The low-temperature behaviour of the heat capacity, including a high value of gamma, along with a deviation from a Curie-Weiss law observed in the low-temperature magnetic susceptibility, are consistent with the presence of magnetic interactions between the paramagnetic interlayer V ions and a Kondo screening of these V moments.