The possibility that free SiO2 may exist at the core mantle boundary motivates a first-principles investigation of the equation of state and possible phase transitions of stishovite using periodic Hartree-Fock theory. Using a moderately extended basis set, the calculated equation of state is shown to be in close agreement with experimental results taken under hydrostatic conditions.When fit to a third-order Birch-Murnaghan equation, the Hartree-Fock total energies give V0=46.1 A3, K0=328 GPa, and K'=4.0. Moreover, the calculated equation of state is very close to that recently obtained using the linearized augmented plane wave method. The bonding in stishovite is unchanged by compression to 80% of its zero-pressure volume (corresponding to a pressure near 110 GPa). The possibility that stishovite might transform to a denser phase at high pressure is investigated by calculating the free energy of SiO2 in the modified-fluorite and α-PbO2 structures. The enthalpy of SiO2 with the fluorite and modified-fluorite structure is too high to allow those structures to be adopted. The 0 K enthalpy of silica in the α-PbO2 structure is within 10 kJ/mol of that of stishovite, and a transition to such a structure cannot be ruled out in the temperature regime of the lower mantle. However, the density of α-PbO2 structure SiO2 is only 2% greater than that of stishovite. ¿ American Geophysical Union 1993