Mean-square atomic displacements in lanthanum triiron cobalt dodecaantimonide, determined as a function of temperature using single-crystal neutron diffraction, show that the La atom exhibits an anomalously large displacement at room temperature, U(eq) = 0.0196 (9) Å(2), because it is too small to fill the atomic cage formed by the corner-linked octahedral framework of M(4)Sb(12), M = Fe, Co. Site-occupancy refinements show 25% vacancies on the La site and an actual Fe:Co ratio of 2.17:1. Analysis of the temperature dependence of the atomic displacements identifies a significant temperature-independent component for the La atom ascribed to static disorder, which amounts to 19% of the room-temperature value. The large-amplitude rattling of the La atom can be effectively linked to the dramatic decrease of the lattice contribution to the thermal conductivity, which is a key factor for improving the thermoelectric behavior of these materials. This structure-property relationship offers a new paradigm for the exploration of thermoelectric materials.