  We define a notion of a viscous shock solution of the stochastic Burgers
equation that connects "top" and "bottom" spatially stationary solutions of the
same equation. Such shocks generally travel in space, but we show that they
admit time-invariant measures when viewed in their own reference frames. Under
such a measure, the viscous shock is a deterministic function of the bottom and
top solutions and the shock location. However, the measure of the bottom and
top solutions must be tilted to account for the change of reference frame. We
also show a convergence result to these stationary shock solutions from
solutions initially connecting two constants, as time goes to infinity.
