Artificial chiral structure plays an important role in the realization of strong chiroptical response and flexible light manipulation. Without introducing intrinsic chiral metamaterial with a complicated structure, we utilize a chiral metasurface to achieve giant extrinsic and tunable terahertz (THz) chirality assisted by quasi-bound states in the continuum (qBIC). The giant extrinsic chirality in this work originates from the mirror symmetry breaking of the proposed plasmonic THz metasurface; owing to the optical properties of InSb, the chirality induced by this metasurface can be actively manipulated by tailoring the angle of the elliptical nanopillar pairs and temperature. This proposed THz qBIC-assisted metasurface opens a new door for the detection of strong chirality, which may find potential important applications in THz science and technology, such as THz spin optics, chiral sensing, and efficient chiral light-emitting devices.