In this paper we investigate the effect of Benjamin-Feir instability on the surface elevation probability distribution. A uniform wave train is unstable to modulational perturbations, giving rise to sidebands in the spectrum of the surface elevation (hence a broadening of the spectrum). Since these sidebands are phase-locked, one should therefore expect deviations fromthe Gaussian probability distribution. To calculate the surface elevation probability distribution, we assume that the end state of the instability is given by a stable cnoidal wave solution. The present effect could play a role in nature; especially, it may be relevant for the description of swell.