We present a new approach to density functional theory, which does not require the calculation of Kohn-Sham orbitals. The computational workload required by our method—which is based on the calculation of selected elements of the Green's function—scales linearly with the volume of the system, thus opening the way to first-principles calculations for very large systems. Some of the problems which still hinder the achievement of this goal are discussed, and possible solutions are outlined. As an application, we calculate the charge density of a model silicon supercell containing 64 atoms slightly displaced at random from equilibrium.