  We study the propagation of a ``pulled'' front with multiplicative noise that
is created by a local perturbation of an unstable state. Unlike a front
propagating into a metastable state, where a separation of time scales for
sufficiently large $t$ creates a diffusive wandering of the front position
about its mean, we predict that for so-called pulled fronts, the fluctuations
are subdiffusive with root mean square wandering $\Delta(t) \sim t^{1/4}$, {\em
not} $t^{1/2}$. The subdiffusive behavior is confirmed by numerical
simulations: For $t \le 600$, these yield an effective exponent slightly larger
than 1/4.
