Brillouin spectroscopy has been used to measure the adiabatic elastic constants of laboratory-grown pure monocrystalline ice Ih at – 3°C. The values obtained were (in units of 108 N/m2): c11 = 136.96 ±0.60, c12 = 69.66± 0.45, c13 = 56.28±0.31, c33 = 147.02±0.68, c44 = 29.59±0.15. Comparison of these values with ultrasonic measurements quoted in the literature reveals no significant acoustic dispersion in ice over frequencies ranging to 1010 Hz. However, the results suggest that the elastic constants of ice may depend on the precise crystal quality and age of a given sample. The low experimental error in the values obtained, along with the inherent versatility of the method, indicate that Brillouin spectroscopy is an effective technique for systematically investigating the elastic properties of ice samples formed under natural conditions.