  Realizing the topological bands of helical states poses a challenge in
studying ultracold atomic gases. Motivated by the recent experimental success
in realizing chiral optical ladders, here we present a scheme for synthesizing
topological quantum matter, especially the quantum spin Hall phase, in the
chiral optical ladders. More precisely, we first establish the synthetic
pseudo-spin-orbit coupling and Zeeman splitting in the chiral ladders. We
analyze the band structure of the ladders exposed to the bichromatic optical
potentials and report the existence of quantum spin Hall phase. We further
identify a rich phase diagram of the bichromatic chiral ladders, illustrating
that our proposal features a large space of system parameters exhibiting a
variety of quantum phase transitions. Our scheme can be readily implemented in
the existing experimental systems and hence provides a new method to engineer
the sophisticated topological bands for cold atomic gases.
