The lattice dynamics of crystalline L-alanine shows unusual features tentatively assigned to a localization of vibrational energy. However, other properties alternatively suggest the existence of a second order phase transition undetected in previous crystallographic work. In this paper, we present the results of a high resolution X-ray diffraction study down to 10 K, together with new structure determinations at intermediate temperatures. The data rule out the hypothesis of a conventional structural phase transition. No change in the space group symmetry is observed and an anomalous decrease of the lattice parameter c in discrete steps is discovered when heating the crystal from 10 K to room temperature. It could be ascribed to a progressive conformational change of the NH₃ ⁺ group of the zwitterionic molecule. An analysis of the physical properties of crystalline L-alanine suggests the existence of a strong dynamic Jahn-Teller-like effect owing to the NH₃ ⁺ charge-lattice coupling. This would explain both the splitting of some vibrational states and properties related to a microscopic lattice instability like the onset of depolarization in the transmitted light below ∼250 K.