  We study chiral and nonreciprocal single-photon scattering in a
chiral-giant-molecule waveguide-QED system. Here, the giant molecule consists
of two coupled giant atoms, which interact with two linear waveguides, forming
a four-port quantum device. We obtain the exact analytical expressions of the
four scattering amplitudes using a real-space method. Under the Markovian
limit, we find that the single-photon scattering behavior is determined by the
coupling strength between the giant atoms and the waveguides, the coupling
strength between the two giant atoms, and the nondipole effect caused by the
phase accumulation of photons travelling between the coupling points. It is
also found that chiral and nonreciprocal single-photon scattering can be
realized by introducing the chiral coupling to break the symmetry in the
coupling configuration between the giant molecule and the waveguides. In
addition, an ideal chiral emitter-waveguide coupling enables a directional
single-photon routing. In the non-Markovian regime, the scattering spectra are
characterized by more abundant structures with multiple peaks and dips. In
particular, we demonstrate that the non-Markovian retarded effect can induce
the nonreciprocal single-photon scattering. Our results have potential
applications in the design of optical quantum devices involving giant atoms,
which can provide an efficient platform for studying chiral quantum optics.
