We report on the first direct measurement of the adiabatic index γ through x-ray Thomson scattering from shock-compressed beryllium. 9 keV x-ray photons probe the bulk properties of matter during the collision of two counterpropagating shocks. This novel experimental technique determines γ by using only the measured mass densities and vanishing particle velocity at the point of shock collision to close the Rankine-Hugoniot equations. We find γ>5/3 at 3× compression, clearly different from ideal gas behavior. At 6× compression, γ shows the convergence to the ideal gas limit, in agreement with linear scaling laws.