The cross-plane thermal conductivity of thin films of WSe2 grown from alternating W and Se layers is as small as 0.05 watts per meter per degree kelvin at room temperature, 30 times smaller than the c-axis thermal conductivity of single-crystal WSe2 and a factor of 6 smaller than the predicted minimum thermal conductivity for this material. We attribute the ultralow thermal conductivity of these disordered, layered crystals to the localization of lattice vibrations induced by the random stacking of two-dimensional crystalline WSe2 sheets. Disordering of the layered structure by ion bombardment increases the thermal conductivity.