We numerically calculate the configurational entropy Sconf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires fewer assumptions than the previous methods (Speedy 1998 Mol.Phys. 95 169). We find that Sconf is a decreasing function of the packing fraction φ and extrapolates to zero at the Kauzmann packing fraction , suggesting the possibility of an ideal glass transition for the hard-sphere system. Finally, the Adam-Gibbs relation is found to hold. © IOP Publishing Ltd.