  An exact superpotential is derived for the N=1 theories which arise as
massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The
superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to
coincide with the complexified potential of the N-body elliptic Calogero-Moser
Hamiltonian. This superpotential reproduces the vacuum structure predicted by
Donagi and Witten for the corresponding four-dimensional theory and also
transforms covariantly under the S-duality group of N=4 SYM. The analysis
yields exact formulae with interesting modular properties for the condensates
of gauge-invariant chiral operators in the four-dimensional theory.
