Methylammonium lead trihalide perovskites CH3NH3PbX3 (X = Cl, Br, and I) have recently attracted huge attention as a promising candidate for highly efficient solar cell absorber materials. To understand the physical properties of halide perovskites, we investigated the CH3NH3PbCl3 single crystal by Raman scattering spectroscopy from 80 K to room temperature. Benchmarking the phonon modes and their Raman activities obtained by density functional calculations, we successfully assign the molecular vibrations of methylammonium in the frequency range from 400 to 3300 cm-1. In the temperature-dependent Raman scattering spectra, the internal vibrational modes of the CH3NH3 + cation are observed in the frequency range above 400 cm-1 and a number of peaks among them show characteristic changes that reflect the phase transition occurring at about 160 K in CH3NH3PbCl3. A noticeable Raman peak at 2900 cm-1 persists in a wide range of temperature, suggesting the existence of microcrystalline methylammonium chloride possibly left on the crystal surface from the growth process or spontaneously formed after synthesis.