  We study one-dimensional fluctuating interfaces of length $L$ where the
interface stochastically resets to a fixed initial profile at a constant rate
$r$. For finite $r$ in the limit $L \to \infty$, the system settles into a
nonequilibrium stationary state with non-Gaussian interface fluctuations, which
we characterize analytically for the Kardar-Parisi-Zhang and Edwards-Wilkinson
universality class. Our results are corroborated by numerical simulations. We
also discuss the generality of our results for a fluctuating interface in a
generic universality class.
