  The integer quantum Hall effect (IQHE) and chaos are commonly conceived as
being unrelated. Contrary to common wisdoms, we find in a canonical chaotic
system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven
phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically,
the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of
critical $h_e$-values, but otherwise bounded ('insulating' phase). The latter
phase is topological in nature and characterized by a quantum number
('quantized Hall conductance'). The number jumps by unity whenever $h_e$
decreases passing through each critical value. Our findings, within the reach
of cold-atom experiments, indicate that rich topological quantum phenomena may
emerge from chaos.
