  We prove that the stochastic Burgers equation on $\mathbf{R}^{d}$, $d<4$,
forced by gradient noise that is white in time and smooth in space, admits
spacetime-stationary solutions. These solutions are thus the gradients of
solutions to the KPZ equation on $\mathbf{R}^{d}$ with stationary gradients.
The proof works by proving tightness of the time-averaged laws of the solutions
in an appropriate weighted space.
