Stoichiometric single-crystal HfN layers grown on MgO(001) are analyzed by Raman spectroscopy. Second-order Raman scattering predominates, but first-order modes in the acoustic and optical ranges are also visible. The latter indicates that the Oh symmetry of NaCl-structure HfN is broken. The large mass difference between Hf and N leads to a correspondingly large separation, 250 cm-1, between the first-order acoustic and optical bands. Within this gap, four Raman lines are clearly observed. The first three are the second-order transverse acoustic mode (240 cm-1), the sum of the first-order transverse and longitudinal acoustic modes (280 cm-1), and the second-order longitudinal acoustic mode (325 cm-1). The fourth line at 380 cm-1 is identified as the difference between the first-order optical and acoustic modes. The observed first-order Raman scattering, as well as the width of the gap between the first-order acoustic and optical modes, is in good agreement with previously calculated HfN phonon density of states.