The elastic constants of high-quality, single-crystal hexagonal boron nitride (h-BN) have been measured by means of high resolution Brillouin spectroscopy using a modified reflected light microscope. The sound propagation velocity in the c-axis direction and perpendicular to the c-axis have been obtained from the Brillouin frequency shift, with a proper account taken of the vast difference between the ordinary and extraordinary refractive indices recently reported in the highly anisotropic layered h-BN crystal. The elastic constants c(11) and c(33) obtained from the Brillouin experiments are somewhat lower than previous determinations based on inelastic x-ray measurements and confirm the overestimation of the h-BN elastic constants by ab initio calculations based on density functional perturbation theory in the local density approximation. Published by AIP Publishing.