The equation of state and structure of CaSiO3 perovskite are determined at high pressures using the density-functional-based Variationally Induced Breathing (VIB) method, modified with a small, parameterized covalent correction to the short-range Si-O interaction. Our thermally corrected room temperature equation of state parameters (V0 = 45.90 ¿ 0.02 ¿, K0 = 228 ¿ 2 GPa, K' = 4.3 ¿ 0.1) are in very good agreement with near-hydrostatic compression data as well as recent calculations based on first-principles methods. We examined the tetragonal, orthorhombic, and triclinic structures, and compared their stabilities relative to the cubic structure at lower mantle pressures. We found that the orthorhombic perovskite structure of CaSiO3 is the thermodynamically stable phase at all mantle pressures. The structural and energy differences between the orthorhombic and cubic lattices under static conditions are small, and increase only slightly with pressure. Consequently, the cubic structure may be thermodynamically stable at lower mantle temperatures.