<p>Chiral and nonreciprocal quantum devices are crucial for signal routing and processing in a quantum network. In this work, we study the chirality and nonreciprocity of a giant atom coupled to a one-dimensional waveguide. We clarify that the chiral emission of the giant atom is not directly related to the time-reversal symmetry breaking but to the mirror-symmetry breaking. We propose a passive scheme, by extending the legs of the giant atom, to realize the chiral emission without breaking time-reversal symmetry. We prove that the time-reversal symmetry breaking alone via nonuniform coupling phases is not sufficient for the nonreciprocal single-photon scattering of the giant atom. The nonreciprocity needs both the time-reversal symmetry breaking and the finite external dissipation of the giant atom. Our work clarifies the roles of symmetries in the chirality and nonreciprocity of giant-atom systems and paves the way for the design of on-chip functional devices with superconducting giant atoms.</p>