A periodically driven quantum Hall system in a fixed magnetic field is found to exhibit a series of phases featuring anomalous edge modes with the wrong chirality. This leads to pairs of counter-propagating chiral edge modes at each edge, in sharp contrast to stationary quantum Hall systems. We show that the pair of Floquet edge modes are protected by the chiral (sublattice) symmetry, and that they are robust against static disorder. The existence of distinctive phases with the same Chern and winding numbers but very different edge state spectra points to the important role played by symmetry in classifying topological properties of driven systems. We further explore the evolution of the edge states with driving using a simplified model, and discuss their experimental signatures.
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