  Optical frequency combs establish a rigid phase-coherent link between
microwave and optical domains and are emerging as high-precision tools in an
increasing number of applications. Frequency combs with large intermodal
spacing are employed in the field of microwave photonics for radiofrequency
arbitrary waveform synthesis and for generation of THz tones of high spectral
purity in the future wireless communication networks. We demonstrate for the
first time self-starting harmonic frequency comb generation with a THz
repetition rate in a quantum cascade laser. The large intermodal spacing caused
by the suppression of tens of adjacent cavity modes originates from a
parametric contribution to the gain due to temporal modulations of the
population inversion in the laser. The mode spacing of the harmonic comb is
shown to be uniform to within $5\times 10^{-12}$ parts of the central frequency
using multiheterodyne self-detection. This new harmonic comb state extends the
range of applications of quantum cascade laser frequency combs.
