A torsional potential energy surface for the cyclic water trimer was calculated at the level of second-order Moller-Plesset perturbation theory. For the construction of this ab initio surface, the first-order wave function was expanded in a many-electron basis which linearly depends on the interelectronic coordinates r(12). The one-electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near-) basis set limit for the level of theory applied. The positions of the free O-H bonds are described by three torsional angles. The respective three-dimensional torsional space was investigated by 70 counterpoise corrected single-point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree-Fock and conventional Moller-Plesset levels [Schutz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail : Relative energies of the structures were calculated by applying second-order Moller-Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second-order Moller-Plesset level with a 6-311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far-infrared vibration-rotation-tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational-tunneling path.