A fluid mixture of hard discs is made glassy in a molecular dynamics experiment by permanently constraining each disc center to stay within a cage of three near neighbors. The constraints can be applied at any density and they cause a thermodynamic glass transition where the compressibility, heat capacity, and entropy decrease. The decrease in entropy provides a direct measure of the configurational entropy of the fluid. A relation between diffusivity and the configurational entropy suggested by Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)] is shown to be accurate from the ideal gas to the kinetic glass transition.