An inelastic neutron scattering investigation of high-temperature quartz by triple-axis spectrometry reveals the existence of a phonon branch with anomalously low and temperature-dependent frequencies. Near the Brillouin zone center, the mode is overdamped and unstable, and gives rise to a critical scattering intensity which diverges as (T-Tc)-1. Here Tc is 10°C lower than the transition temperature T0=573°C. Measurements of the relative intensity of the critical scattering about various reciprocal-lattice points establishes that the general pattern of displacements associated with the - transformation is determined by this soft mode. At room temperature, the zone center phonon at 25.8 meV (208 cm-1) is shown to strongly resemble the - displacements. This confirms the proposal by Scott that the renormalized soft mode interacts with and passes through another low-lying excitation. It is suggested that the anomalous elastic behavior of quartz results from virtual excitation of pairs of phonons in the soft branch with wave vectors directed oppositely along the hexagonal axis. © 1970 The American Physical Society.