We present a method for performing electronic structure calculations without the explicit use of a basis. We combine a finite-difference approach with ab initio pseudopotentials. In contrast to methods which use a plane wave basis, our calculations are performed completely in ''real space.'' No artifacts such as supercell geometries need be introduced for localized systems. Although this approach is easier to implement than one with a plane wave basis, no loss of accuracy occurs. The electronic structure of several diatomic molecules, Si2, C2, O2, and CO, are calculated to illustrate the utility of this method.