The elastic constants of natural single-crystal aragonite (CaCO3) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C-11, C-22, C-33, C-44, C-55, C-66, C-12, C-13 and C-23 are 171.1 1.0, 110.1 0.9, 98.4 1.2, 39.3 0.6, 24.2 0.4, 40.2 0.6, 60.3 1.0, 27.8 1.6 and 41.9 2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0 0.2, 4.2 0.2 and 7.3 0.6x10(-3) GPa(-1), respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9 1.4 and 35.8 0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies.