  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.
