S-Duality and Cosmological Constant in String Theory

The S-duality invariance of the equations of motion of four dimensional string effective action with cosmological constant, $\Lambda $, is studied. It is demonstrated that the S-duality symmetry of the field equations are broken for nonzero $\Lambda$. The ``naturalness'' hypothesis is invoked to argue that $\Lambda $ should remain small since exact S-duality symmetry will force the cosmological constant to vanish in the string effective action.