We consider the Cahn-Hilliard equation in one space dimension, perturbed by the derivative of a space and time white noise of intensity $epsilon^{frac 12}$, and we investigate the effect of the noise, as $epsilon to 0$, on the solutions when the initial condition is a front that separates the two stable phases. We prove that, given $gamma< frac 23$, with probability going to one as $epsilon to 0$, the solution remains close to a front for times of the order of $epsilon^{-gamma}$, and we study the fluctuations of the front in this time scaling. They are given by a one dimensional continuous process, self similar of order $frac 14$ and non Markovian, related to a fractional Brownian motion and for which a couple of representations are given.
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