Engineering of materials with specific physical properties has recently focused on the effect of nano-sized 'guest domains' in a 'host matrix' that enable tuning of electrical, mechanical, photo-optical or thermal properties. A low thermal conductivity is a prerequisite for obtaining effective thermoelectric materials, and the challenge is to limit the conduction of heat by phonons, without simultaneously reducing the charge transport. This is named the 'phonon glass-electron crystal' concept and may be realized in host-guest systems. The guest entities are believed to have independent oscillations, so-called rattler modes, which scatter the acoustic phonons and reduce the thermal conductivity. We have investigated the phonon dispersion relation in the phonon glass-electron crystal material Ba(8)Ga(16)Ge(30) using neutron triple-axis spectroscopy. The results disclose unambiguously the theoretically predicted avoided crossing of the rattler modes and the acoustic-phonon branches. The observed phonon lifetimes are longer than expected, and a new explanation for the low kappa(L) is provided.