The single-crystal elastic constants of SiO₂, coesite (monoclinic, C2/c), have been determined from Brillouin scattering measurements on a 100-μm crystal. The elastic constants inferred from acoustic velocities for 80 different propagation directions are (in units of Mbar) c₁₁ = 1.608, c₂₂ = 2.304, c₃₃ = 2.316, c₄₄ = 0.678, c₅₅ = 0.733, c₆₆ =0.588, c₁₂ = 0.821, c₁₃ = 1.029, c₁₅ = −0.362, c₂₃ = 0.356, c₂₅ = 0.026, c₃₅ = −0.393, and c₄₆ = 0.099. This experimental technique provides a method of determining single-crystal elastic properties for materials such as high-pressure phases that are not available in sufficiently large sizes for ultrasonic measurements.