  We propose tunable chiral bound states in a system composed of
superconducting giant atoms and a Josephson photonic-crystal waveguide (PCW),
with no analog in other quantum setups. The chiral bound states arise due to
interference in the nonlocal coupling of a giant atom to multiple points of the
waveguide. The chirality can be tuned by changing either the atom-waveguide
coupling or the external bias of the PCW. Furthermore, the chiral bound states
can induce directional dipole-dipole interactions between multiple giant atoms
coupling to the same waveguide. Our proposal is ready to be implemented in
experiments with superconducting circuits, where it can be used as a tunable
toolbox to realize topological phase transitions and quantum simulations.
