Broadband (1.6–18 THz) terahertz time-domain spectroscopy (THz-TDS) and time-resolved terahertz spectroscopy (TRTS) were performed on a 54 μm thick chalcogenide glass (As30Se30Te40) sample with a two-color laser-induced air plasma THz system in transmission and reflection modes, respectively. Two absorption bands at 2–3 and 5–8 THz were observed. TRTS reveals an ultrafast relaxation process of the photoinduced carrier response, well described by a rate equation model with a finite concentration of mid-bandgap trap states for self-trapped excitons. The photoinduced conductivity can be well described by the Drude–Smith conductivity model with a carrier scattering time of 12–17 fs, and we observe significant carrier localization effects. A fast refractive index change was observed 100 fs before the conductivity reached its maximum, with 2 orders of magnitude larger amplitude than expected for the optically induced THz Kerr effect, indicating that free carriers are responsible for the transient index change.