The desire for intrinsically low lattice thermal conductivity (κL) in thermoelectrics motivates numerous efforts on understanding the microscopic mechanisms of heat transport in solids. Here, based on theoretical calculations, we demonstrate that α-MgAgSb hosts low-energy localized phonon bands and avoided crossing of the rattler modes, which coincides with the inelastic neutron scattering result. Using the two-channel lattice dynamical approach, we find, besides the conventional contribution (∼70% at 300 K) from particlelike phonons propagating, the coherence contribution dominated by the wavelike tunneling of phonons accounts for ∼30% of the total κL at 300 K. By considering dual contributions, our calculated room-temperature κL of 0.64 W m−1 K−1 well agrees with the experimental value of 0.63 W m−1 K−1. More importantly, our computations give a nonstandard κL ∝ T−0.61 dependence, perfectly explaining the abnormal temperature-trend of ∼T−0.57 in experiment for α-MgAgSb. By molecular dynamics simulation, we reveal that the structure simultaneously has soft crystalline sublattices with the metavalent bonding and fluctuating liquid-like sublattices with thermally induced large amplitude vibrations. These diverse forms of chemical bonding arouse mixed part-crystal part-liquid state, scatter strongly heat-carrying phonons, and finally produce extremely low κL. The fundamental research from this study will accelerate the design of ultralow-κL materials for energy-conversion applications.