The six independent second-order elastic stiffness coefficients of a Ti44Al56 single crystal (L10 structure) have been measured at room temperature for the first time using a resonant ultrasonic spectroscopy (RUS) technique. These data were used to calculate the orientation dependence of Young's modulus and the shear modulus. Young's modulus is found to reach a maximum near a [111] direction, close to the normal to the most densely packed planes. The elastic moduli and Poisson's ratio for polycrystalline materials, calculated by the averaging scheme proposed by Hill, are in good agreement with experimental data and theoretical calculations.