The need for both high electrical conductivity and low thermal conductivity creates a design conflict for thermoelectric systems, leading to the consideration of materials with complicated crystal structures(1). Rattling of ions in cages results in low thermal conductivity(2-5), but understanding the mechanism through studies of the phonon dispersion using momentum-resolved spectroscopy is made difficult by the complexity of the unit cells(6). We have performed inelastic X-ray and neutron scattering experiments that are in remarkable agreement with our first-principles density-functional calculations of the phonon dispersion for thermoelectric Na0.8CoO2, which has a large-period superstructure(7). We have directly observed an Einstein-like rattling mode at low energy, involving large an harmonic displacements of the sodium ions inside multi-vacancy clusters. These rattling modes suppress the thermal conductivity by a factor of six compared with vacancy-free NaCoO2. Our results will guide the design of the next generation of materials for applications in solid-state refrigerators and power recovery.