We have measured the spectral linewidths of three continuous-wave quantum cascade lasers operating at terahertz frequencies by heterodyning the free-running quantum cascade laser with two far-infrared gas lasers. Beat notes are detected with a GaAs diode mixer and a microwave spectrum analyzer, permitting very precise frequency measurements and giving instantaneous linewidths of less than -30 kHz. Characteristics are also reported for frequency tuning as the injection current is varied.