The phonon spectrum of a MgAl2O4 spinel has been calculated from first principles using density-functional theory. The spinel was perfectly ordered with space group Fd3m. The five Raman active and four infrared active modes allowed by symmetry are umambiguously identified. Agreement with available Raman, infrared, and inelastic neuron scattering dat is good. The fifth Raman mode (missing in experiment) is located at 570 cm-1.