A new spectrometer allowing both high resolution and broadband coverage in the terahertz (THz) domain is proposed. This instrument exploits the heterodyne technique between broadband synchrotron radiation and a quantum-cascade-laser-based molecular THz laser that acts as the local oscillator. Proof of principle for exploitation for spectroscopy is provided by the recording of molecular absorptions of hydrogen sulfide (H$_2$S) and methanol (CH$_3$OH) around 1.073 THz. Ultimately, the spectrometer will enable to cover the 1–4 THz region in 5 GHz windows at Doppler resolution.