For the first time, the terahertz transmittance spectra of l-alanine have been measured using a single crystal. Measurements were obtained over a large temperature range (12-300 K) and revealed 18 absorptions between 20 and 250 cm-1. These modes were sharp and symmetric, a feature of single crystals and low temperatures. The spectra were directly compared to those of a powdered pellet sample. Raman spectroscopy and x-ray diffraction were used to confirm the sample's structure and purity. With increasing temperature, all modes exhibit spectral redshift, well described by a Bose-Einstein model, indicating the phonon origin of the absorptions. The exceptions are the 91 and 128 cm-1 modes. The former blueshifts. The latter initially blueshifts but transitions to redshifting. Both behaviors are anomalous. Density-functional theory modeling helped assign all the observed modes.