DescriptionReplication of critical data structures in the MPI-only GAMESS Hartree-Fock algorithm limits the full utilization of the manycore Intel Xeon Phi processor. In this work, modern OpenMP threading techniques are used to implement hybrid MPI/OpenMP algorithms. Two separate implementations that differ by the sharing and replication details of key data structures among threads are considered. The hybrid MPI/OpenMP implementations reduce the memory footprint by approximately 200 times compared to the legacy code. The MPI/OpenMP code was shown to run up to six times faster than the original for a range of molecular system sizes. The implementation details and stratgeies will be presented for both hybrid algorithms. Benchmark scaling results results utilizing up to 3000 Intel Xeon Phi processors will also be discussed.