  We study single-photon scattering spectra of a giant atom chirally coupled to
a one-dimensional waveguide at multiple connection points, and examine
chirality induced effects in the scattering spectra. We show that the
transmission spectra typically possess an anti-Lorentzian lineshape with a
nonzero minimum, but by engineering the chirality of the multi-point coupling,
the transmission spectrum of an incident photon can undergo a transition from
complete transmission to total reflection at multiple frequency ``windows'',
where the width of the anti-Lorentzian lineshape for each of the window can be
flexibly tuned at a fixed frequency detuning. Moreover, we show that a perfect
nonreciprocal photon scattering can be achieved due to the interplay between
internal atomic spontaneous emission and the chirally external decay to the
waveguide, in contrast to that induced by the non-Markovian retardation effect.
We also consider the non-Markovian retardation effect on the scattering
spectra, which allows for a photonic band gap even with only two chiral
coupling points. The giant-atom-waveguide system with chiral coupling is a
promising candidate for realizing single-photon routers with multiple channels.
