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　multipoint　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　antiLorentzian　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　nonMarkovian　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.