Topological gauge theories describe the low-energy properties of certain strongly correlated quantum systems through effective weakly interacting models1,2. 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 field3. 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 interactions4. 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 theory5,6,7) 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 interactions8,9,10,11, 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 aÂ route toÂ the implementation of analogous gauge theories in higher dimensions12.