Periodically driven quantum systems can realize phases of matter that do not appear in time-independent Hamiltonians. One application is the engineering of synthetic gauge fields, which enables the study of topological many-body physics with neutral atom quantum simulators. Here we realize the strongly interacting Mott–Meissner phase—a state combining interaction-induced localization with chiral currents induced by an artificial magnetic field—in large-scale bosonic flux ladders with 48 sites at half-filling using a neutral atom quantum simulator. By combining quantum gas microscopy with local basis rotations, we reveal the emerging equilibrium particle currents with local resolution across large systems. We find chiral currents exhibiting a characteristic interaction scaling, providing direct experimental evidence of the interacting Mott–Meissner phase. Moreover, we benchmark density correlations with numerical simulations and find that the effective temperature of the system is on the order of the tunnel coupling. These results establish the feasibility of scaling periodically driven quantum systems to large, strongly correlated phases, enabling further studies of topological quantum matter with single-atom resolution and control.