Incoherent Inelastic Neutron Scattering data and new infrared spectra were acquired in order to examine both the external and internal vibrations in crystalline L-alanine. For the first time we observe a splitting of the NH₃⁺ torsional band below a temperature of approximately 220 K as well as an overtone of this band. The intensity of both of these bands is strongly dependent on temperature. Birefringence and depolarization measurements performed with single crystals reveal a subtle breaking of symmetry around 220 K perhaps involving the hydrogen bond networks. We show that this instability cannot, however, be the origin of the observed splitting. Instead, the anomalous temperature dependence of the observed intensity and frequency of the torsional mode and its overtone may be explained on the basis of a nonlinear coupling of the NH₃⁺ oscillator with lattice phonons. This leads to localization of vibrational energy, a so-called "breather" or "vibrational polaron".