The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional driven open dy
namics with a Chern insulator steady state. Within a Keldysh field theory approach, we show that under mild assumptions - particle number conservation and purity of the stationary state - an abelian Chern-Simons theory describes its response to external perturbations. As a corollary, we predict chiral edge modes stabilized by a dissipative bulk.
