We realized a tunable continuous-wave terahertz source with megahertz frequency resolution. The system is based on optical heterodyning of two near-infrared distributed feedback diode lasers, each laser being stabilized by electronic feedback from a low-finesse quadrature interferometer. The control loop permits precisely linear laser frequency scans over >1200 GHz, and a beat signal linewidth of 1 MHz at 80 ms time scale. Using GaAs photomixers and log-periodic antennae, we achieve a signal-to-noise ratio of the terahertz power of >70 dB at 100 GHz and 100 ms integration time, and still approximately 30 dB at 1 THz. As an example for high-resolution terahertz spectroscopy, we characterize the transmission properties of a subwavelength metal grating.