We have used Almlof and Haser＇s Laplace transform idea to eliminate the energy denominator in second-order perturbation theory (MP2) and obtain an energy expression in the atomic orbital basis. We show that the asymptotic computational cost of this method scales quadratically with molecular size. We then define atomic orbital domains such that selective pairwise interactions can be neglected using well-defined thresholding criteria based on the power law decay properties of the long-range contributions. For large molecules, our scheme yields linear scaling computational cost as a function of molecular size. The errors can be controlled in a precise manner and our method reproduces canonical MP2 energies. We present benchmark calculations of polyglycine chains and water clusters containing up to 3040 basis functions.