Studying periodic systems using electronic structure theory has great importance in solid-state chemistry and physics. However, development of quantum chemical methods for periodic systems has been hampered for decades due to the unaffordable scaling with system size. One limiting step in methods like Hartree—Fock (HF) and hybrid density functional theory (DFT) is the evaluation of two-electron repulsion integrals that are involved in the Coulomb and exchange terms. In this work, an efficient parallel implementation of a local density fitting technique is presented in which product density is approximated using only auxiliary basis functions with the same centers as atomic orbitals in that product. We applied this approach to the exchange term in HF within periodic boundary conditions (periodic HF) based on atom-centered Gaussian-type orbitals, leading to a significant decrease in the computational cost with errors below millihartree per atom.