Thresholding criteria are introduced that enforce locality of exchange interactions in Cartesian Gaussian-based Hartree-Fock calculations. These criteria are obtained from an asymptotic form of the density matrix valid for insulating systems, and lead to a linear scaling algorithm for computation of the Hartree-Fock exchange matrix. Restricted Hartree-Fock/3-21G calculations on a series of water clusters and polyglycine alpha-helices are used to demonstrate the O(N) complexity of the algorithm, its competitiveness with standard direct self-consistent field methods, and a systematic control of error in converged total energies.