We present a new linear scaling method for electronic structure computations in the context of Kohn-Sham density functional theory (DFT). The method is based on a subspace iteration, and takes advantage of the non-orthogonal formulation of the Kohn-Sham functional, and the improved localization properties of non-orthogonal wave functions. We demonstrate the efficiency of the algorithm for practical applications by performing fully three-dimensional computations of the electronic density of alkane chains. This is joint work with Jianfeng Lu, Yulin Xuan, and Weinan E, at Princeton University.