Ocean general circulation models (OGCMs) are often used at horizontal resolutions that preclude the appearance of mesoscale eddies. The ocean mesoscale constitutes a significant component of ocean variability, and OGCMs whose resolutions are too coarse to represent the mesoscale are necessarily lacking this variability. In addition to being variable, the ocean mesoscale also induces variability on larger scales that could be resolved on a coarse grid, but coarse OGCMs often lack this variability too. This paper develops a stochastic parameterization that adds small increments to an OGCM’s lateral velocity field, which excites natural modes of variability in the model. The rate at which these velocity increments add energy to the flow is tied to the rate at which the Gent-McWilliams parameterization – a popular parameterization of the effect of mesoscale eddies on tracer transport – removes potential energy from the resolved scales. The stochastic parameterization is implemented in a non-eddying OGCM, where it is shown to increase the variability significantly.