The elastic constants of ice VI have been determined at -2 degrees C and 7.2 kbar by single crystal Brillouin spectroscopy. The adiabatic elastic moduli were found to be C-11 = 26.8, C-12 = 14.5, C-13 = 12.8, C-33 = 26.2, C-44 = 6.3, and C-66 = 10.4 x 10(4) bar, within approximately 1.5%. Large (125 mm(3)) single crystals were grown in a high pressure cell and in situ Brillouin spectra were collected at various crystal orientations about the laboratory z-axis. Ice VI crystals were oriented, while under pressure, by using the birefringent properties and Brillouin spectral behavior. Several polycrystalline elastic properties are derived using the bulk adiabatic moduli and a comparison with previous results is made.