  Topological gauge theories describe the low-energy properties of certain
strongly correlated quantum systems through effective weakly interacting
models. A prime example is the Chern-Simons theory of fractional quantum Hall
states, where anyonic excitations emerge from the coupling between weakly
interacting matter particles and a density-dependent gauge field. Although in
traditional solid-state platforms such gauge theories are only convenient
theoretical constructions, engineered quantum systems enable their direct
implementation and provide a fertile playground to investigate their
phenomenology without the need for strong interactions. Here, we report the
quantum simulation of a topological gauge theory by realizing a one-dimensional
reduction of the Chern-Simons theory (the chiral BF theory) in a Bose-Einstein
condensate. Using the local conservation laws of the theory, we eliminate the
gauge degrees of freedom in favour of chiral matter interactions, which we
engineer by synthesizing optically dressed atomic states with
momentum-dependent scattering properties. This allows us to reveal the key
properties of the chiral BF theory: the formation of chiral solitons and the
emergence of an electric field generated by the system itself. Our results
expand the scope of quantum simulation to topological gauge theories and open a
route to the implementation of analogous gauge theories in higher dimensions.
