We demonstrate the phase locking of a 2.7 THz metal-metal waveguide quantum cascade laser (QCL) to an external microwave signal. The reference is the 15th harmonic, generated by a semiconductor superlattice nonlinear device, of a signal at 182 GHz, which itself is generated by a multiplier chain ͑ϫ12͒ from a microwave synthesizer at ϳ15 GHz. Both laser and reference radiations are coupled into a bolometer mixer, resulting in a beat signal, which is fed into a phase-lock loop. The spectral analysis of the beat signal confirms that the QCL is phase locked. This result opens the possibility to extend heterodyne interferometers into the far-infrared range. To proceed with the applications of terahertz QCLs as LOs in a heterodyne spectrometer, the stabilization of the frequency or phase is required to either eliminate the frequency jitter or to reduce the phase noise. For a heterodyne interferometer either on the earth [4] or in space [5], the phase locking of multiple LOs to a common reference at low frequency is essential. Phase locking [6] a laser to a reference means to control the phase of the laser radiation field precisely. This serves not only to stabilize the frequency but also to transfer the line profile of the reference to the laser. In the case of frequency locking, the laser's average frequency is fixed, but its linewidth remains equal to the laser's intrinsic linewidth. Several experiments to stabilize a terahertz QCL have been published. They are the frequency locking of a 3.1 THz QCL to a far-infrared (FIR) gas laser [7], the phase locking of the beat signal of two lateral modes of a terahertz QCL to a microwave reference [8], and the phase locking of a 1.5 THz QCL to a multiplier chain LO source [9]. Since the multiplier chain source has been demonstrated only up to about 2 THz, for a practical solution for the use of a QCL as LO beyond this frequency, the phase needs to be locked to an external reference that can be generated conveniently and should preferably be far below the QCL frequency. Therefore, an important challenge is the demonstration of the phase locking of a singlemode terahertz QCL to a microwave reference signal (MRS), which is the scheme commonly used in existing solid-state LOs. The MRS should be multiplied to a terahertz frequency in the vicinity of the laser frequency to obtain a beat note or an intermediate frequency (IF). As demonstrated in the measurements of FIR gas laser frequency, the harmonics of MRS at 3.8 THz [10] and at 4.3 THz [11] can be generated by Josephson junction harmonic mixers, resulting in a beat between the laser and the upconverted frequencies. Another commonly used harmonic generator is a Schottky diode [12].In this Letter, we report the phase locking of a 2.7 THz QCL to a harmonic generated from an MRS by a semiconductor superlattice (SL) nonlinear device in combination with a multiplier chain. We demonstrate a practical phase-locking scheme that is extendable to a much higher frequency and quantify the phaselocked power.The QCL used is based on the doubl...