Films containing 8, 16, 24, 32 and 64 MoSe2 layers were synthesized using the modulated elemental reactants method. X-ray reflectivity patterns showed that the annealed films were the targeted number of MoSe2 layers thick with atomically smooth interfaces. In-plane x-ray diffraction (XRD) scans contained only hk0 reflections for crystalline MoSe2 monolayers. Specular XRD patterns contained only 00l reflections, also indicating that the hk0 plane of the MoSe2 layers are parallel to the substrate. Both XRD and electron microscopy techniques indicated that the hk0 planes are rotationally disordered with respect to one another, with all orientations equally probable for large areas. The rotational disorder between MoSe2 layers is present even when analyzed spots are within 10 nm of one another. Cross-plane thermal conductivities of 0.07-0.09 W m-1 K-1 were measured by time domain thermoreflectance, with the thinnest films exhibiting the lowest conductivity. The structural analysis suggests that the ultralow thermal conductivity is a consequence of rotational disorder, which increases the separation between MoSe2 layers. The bonding environment of the Se atoms also becomes significantly distorted from C 3v symmetry due to the rotational disorder between layers. This structural disorder efficiently reduces the group velocity of the transverse phonon modes but not that of longitudinal modes. Since rotational disorder between adjacent layers in heterostructures is expected if the constituents have incommensurate lattices, this study indicates that these heterostructures will have very low cross-plane thermal conductivity.